All Stories

  1. Closed-form formulas of two Gauss hypergeometric functions of specific parameters
  2. Several Derivative Formulas of Two Exponential Functions and Real Power of Hyperbolic Secant Function with a Generalization of a Formula for Specific Partial Bell Polynomials
  3. Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function
  4. Power Series Expansions of Real Powers of Inverse Cosine and Sine Functions, Closed-Form Formulas of Partial Bell Polynomials at Specific Arguments, and Series Representations of Real Powers of Circular Constant
  5. Some Properties on Normalized Tails of Maclaurin Power Series Expansion of Exponential Function
  6. Розвинення функції $\ln(1+\operatorname{e}^x)$ у степеневий ряд через ета-функцію Діріхле та числа Стірлінга другого роду
  7. Monotonicity Results of Ratios Between Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine
  8. A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments
  9. Some Properties of Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine
  10. Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions
  11. Reformulations and Generalizations of Hoffman’s and Genčev’s Combinatorial Identities
  12. On normalized tails of series expansion of generating function of Bernoulli numbers
  13. Toeplitz Operators on Harmonic Fock Spaces with Radial Symbols
  14. A logarithmically completely monotonic function and several inequalities for q-multinominal coefficients and q-multivariate beta functions
  15. On Bounds for Norms of Sine and Cosine Along a Circle on the Complex Plane
  16. Power series expansion, decreasing property, and concavity related to logarithm of normalized tail of power series expansion of cosine
  17. Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function
  18. On convexity and power series expansion for logarithm of normalized tail of power series expansion for square of tangent
  19. Necessary and sufficient conditions for a mixed bivariate mean of three parameters to be Schur m-power convex
  20. On signs of certain Toeplitz-Hessenberg determinants whose elements involve Bernoulli numbers
  21. Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions
  22. Approximation by multivariate Baskakov–Durrmeyer operators in Orlicz spaces
  23. Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function
  24. A Series Expansion of a Logarithmic Expression and a Decreasing Property of the Ratio of Two Logarithmic Expressions Containing Sine
  25. Determinantal Expressions, Identities, Concavity, Maclaurin Power Series Expansions for van der Pol Numbers, Bernoulli Numbers, and Cotangent
  26. A Sufficient and Necessary Condition for the Power-Exponential Function 1+1xαx to Be a Bernstein Function and Related nth Derivatives
  27. Negativity, zeros and extreme values of several polynomials
  28. Some combinatorial identities containing central binomial coefficients or Catalan numbers*
  29. The negativity of a polynomial of degree forty-three
  30. A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations
  31. Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means
  32. Closed-Form Formulas for the nth Derivative of the Power-Exponential Function xx
  33. Integral representations and properties of several finite sums containing central binomial coefficients
  34. Alternative Proofs for Monotonicity of Some Functions Related to Sectional Curvature of Fisher–Rao Manifold of Beta Distributions
  35. NOTES ON SOME SIMPSON TYPE INTEGRAL INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTIONS WITH APPLICATIONS
  36. Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
  37. Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark–İsmail’s two conjectures
  38. A series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine
  39. Three identities and a determinantal formula for differences between Bernoulli polynomials and numbers
  40. Series expansions for powers of sinc function and closed-form expressions for specific partial bell polynomials
  41. A further generalization of the Catalan numbers and its explicit formula and integral representation
  42. Specific values of partial bell polynomials and series expansions for real powers of functions and for composite functions
  43. Increasing property and logarithmic convexity concerning Dirichlet beta function, Euler numbers, and their ratios
  44. Several recursive and closed-form formulas for some specific values of partial Bell polynomials
  45. Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol–Bernoulli Polynomials and Numbers, and Degenerate Apostol–Euler Polynomials and Numbers
  46. Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
  47. Necessary and Sufficient Conditions for a Bivariate Mean of Three Parameters to Be the Schur $m$-Power Convex
  48. Several recurrence relations and identities on generalized derangement numbers
  49. Notes on several integral inequalities of Hermite–Hadamard type for s-geometrically convex functions
  50. Necessary and Sufficient Conditions for a Difference Defined by Four Derivatives of a Function Containing Trigamma Function to be Completely Monotonic
  51. Complete Monotonicity for a New Ratio of Finitely Many Gamma Functions
  52. Decreasing properties of two ratios defined by three and four polygamma functions
  53. On Degenerate Array Type Polynomials
  54. Bounds for completely monotonic degrees of remainders in asymptotic expansions of the digamma function
  55. MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function
  56. Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities
  57. Increasing property and logarithmic convexity of two functions involving Dirichlet eta function
  58. Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution
  59. Refinements of two determinantal inequalities for positive semidefinite matrices
  60. Taylor’s series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of Pi
  61. Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind
  62. A further generalization of the Catalan numbers and its explicit formula and integral representation
  63. Discussions on two integral inequalities of Hermite–Hadamard type for convex functions
  64. A determinantal expression and a recursive relation of the Delannoy numbers
  65. Explicit formulas for partial Bell polynomials, Maclaurin's series expansions of real powers of inverse (hyperbolic) cosine and sine, and series representations of powers of Pi
  66. Maclaurin's series expansions of real powers of inverse (hyperbolic) cosine and sine functions with applications
  67. Lower Bound of Sectional Curvature of Fisher–Rao Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions
  68. Maclaurin's series expansions of real powers of inverse (hyperbolic) cosine functions and applications
  69. Two Explicit Formulas for Degenerate Peters Numbers and Polynomials
  70. A closed-form expression of a remarkable sequence of polynomials originating from a family of entire functions connecting the Bessel and Lambert functions
  71. Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios
  72. Several closed and determinantal forms for convolved Fibonacci numbers
  73. Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences
  74. Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function
  75. Two determinantal inequalities for positive semidefinite matrices
  76. Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials
  77. Some properties of the Hermite polynomials
  78. A ratio of finitely many gamma functions and its properties with applications
  79. Simplifying coefficients in differential equations related to generating functions of reverse Bessel and partially degenerate Bell polynomials
  80. Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function
  81. Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions
  82. Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers
  83. Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices
  84. Bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function
  85. Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind
  86. Determinantal Formulas and Recurrent Relations for Bi-Periodic Fibonacci and Lucas Polynomials
  87. Integral inequalities of Hermite-Hadamard type for GA-$ F $-convex functions
  88. Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic
  89. Computation of several Hessenberg determinants
  90. Monotonicity and sharp inequalities related to complete (p,q)-elliptic integrals of the first kind
  91. Refinements of Young’s Integral Inequality via Fundamental Inequalities and Mean Value Theorems for Derivatives1
  92. Several Explicit and Recurrent Formulas for Determinants of Tridiagonal Matrices via Generalized Continued Fractions
  93. Complete monotonicity of a difference constituted by four derivatives of a function involving trigamma function
  94. Complete monotonicity of a difference defined by four derivatives of a function containing trigamma function
  95. Lower Bound of Sectional Curvature of Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions
  96. Monotonicity and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
  97. Necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic
  98. Monotonicity of a ratio involving trigamma and tetragamma functions
  99. Geometric interpretations and reversed versions of Young's integral inequality
  100. Some properties of several functions involving polygamma functions and originating from the sectional curvature of the beta manifold
  101. Retraction Note to: A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant
  102. A further generalization of the Catalan numbers and its explicit formula and integral representation
  103. A further generalization of the Catalan numbers and its explicit formula and integral representation
  104. Determinantal forms and recursive relations of the Delannoy two-functional sequence
  105. A further generalization of the Catalan numbers and its explicit formula and integral representation
  106. Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
  107. From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
  108. Inequalities for generalized eigenvalues of quaternion matrices
  109. Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
  110. Several determinantal expressions of generalized Tribonacci polynomials and sequences
  111. Several closed and determinantal forms for convolved Fibonacci numbers
  112. Computation of several Hessenberg determinants
  113. Three closed forms for convolved Fibonacci numbers
  114. Determinantal forms and recursive relations of the Delannoy two-functional sequence
  115. Special values of the Bell polynomials of the second kind for some sequences and functions
  116. Monotonicity, convexity and inequalities related to complete $(p,q,r)$-elliptic integrals and generalized trigonometric functions
  117. Closed formulas and identities on the Bell polynomials and falling factorials
  118. Monotonicity properties for a ratio of finite many gamma functions
  119. Determinantal formulas and recurrent relations for bi-periodic Fibonacci and Lucas polynomials
  120. Some properties and an application of multivariate exponential polynomials
  121. On Bounds of the Sine and Cosine along a Circle on the Complex Plane
  122. On HT-convexity and Hadamard-type inequalities
  123. Completely monotonic degree of a function involving trigamma and tetragamma functions
  124. Correction: Monotonicity and inequalities related to complete elliptic integrals of the second kind
  125. Monotonicity and inequalities related to complete elliptic integrals of the second kind
  126. Several explicit and recursive formulas for generalized Motzkin numbers
  127. Some inequalities and an application of exponential polynomials
  128. Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions
  129. Approximation by multivariate Baskakov–Kantorovich operators in Orlicz spaces
  130. Closed formulas for special bell polynomials by Stirling numbers and associate Stirling numbers
  131. SEVERAL NEW INTEGRAL INEQUALITIES OF THE SIMPSON TYPE FOR(<i>α, S, M</i> )-CONVEX FUNCTIONS
  132. Some inequalities of the Grüss type for conformable $${\varvec{k}}$$k-fractional integral operators
  133. On bounds of the sine and cosine along straight lines on the complex plane
  134. Relations among Bell polynomials, central factorial numbers, and central Bell polynomials
  135. Simplifying coefficients in differential equations for generating function of Catalan numbers
  136. Generalizations and applications of Young’s integral inequality by higher order derivatives
  137. Equivalent theorem of approximation by linear combination of weighted Baskakov–Kantorovich operators in Orlicz spaces
  138. Monotonicity properties and inequalities related to generalized Grötzsch ring functions
  139. Generalizations of Several Inequalities Related to Multivariate Geometric Means
  140. A Closed Formula for the Horadam Polynomials in Terms of a Tridiagonal Determinant
  141. Some fractional differential equations involving generalized hypergeometric functions
  142. A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant
  143. Generalized fractional integral inequalities of Hermite–Hadamard type for ( α , m ...
  144. A Unified Generalization of the Catalan, Fuss, and Fuss–Catalan Numbers
  145. Completely monotonic degrees for a difference between the logarithmic and psi functions
  146. Determinantal expressions and recurrence relations for Fubini and Eulerian polynomials
  147. Some inequalities of the Turan type for confluent hypergeometric functions of the second kind
  148. On complete monotonicity for several classes of functions related to ratios of gamma functions
  149. Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind
  150. Simplifying coefficients in a family of nonlinear ordinary differential equations
  151. Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function
  152. Convexity and inequalities related to extended beta and confluent hypergeometric functions
  153. Generalized k-fractional conformable integrals and related inequalities
  154. Notes on two kinds of special values for the Bell polynomials of the second kind
  155. Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind
  156. Some integral transforms of the generalized k-Mittag-Leffler function
  157. The inverse of a triangular matrix and several identities of the Catalan numbers
  158. Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds
  159. Shannon Type Inequalities for Kapur’s Entropy
  160. On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces
  161. Some Symmetric Identities Involving the Stirling Polynomials Under the Finite Symmetric Group
  162. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers
  163. Alternative proofs of some formulas for two tridiagonal determinants
  164. Some Properties of the Fuss–Catalan Numbers
  165. On integral inequalities of the Hermite–Hadamard type for co-ordinated (α, m1)-(s, m2)-convex functions
  166. Some Inequalities of Čebyšev Type for Conformable k-Fractional Integral Operators
  167. A double inequality for the ratio of two non-zero neighbouring Bernoulli numbers
  168. Integral Inequalities of Hermite–Hadamard Type for Extended s-Convex Functions and Applications
  169. On Bounds of the Sine and Cosine Along Straight Lines on the Complex Plane
  170. On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function
  171. Some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices
  172. Several series identities involving the Catalan numbers
  173. Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function
  174. An Improper Integral, the Beta Function, the Wallis Ratio, and the Catalan Numbers
  175. Some Properties and Generalizations of the Catalan, Fuss, and Fuss-Catalan Numbers
  176. On multivariate logarithmic polynomials and their properties
  177. Simple forms for coefficients in two families of ordinary differential equations
  178. Integral Representations of the Large and Little Schröder Numbers
  179. Some identities for a sequence of unnamed polynomials connected with the Bell polynomials
  180. Integral representations for multivariate logarithmic polynomials
  181. Some new inequalities of the Grüss type for conformable fractional integrals
  182. A diagonal recurrence relation for the Stirling numbers of the first kind
  183. An integral representation, complete monotonicity, and inequalities of the Catalan numbers
  184. Lévy-Khintchine representation of Toader-Qi mean
  185. Some identities related to Eulerian polynomials and involving the Stirling numbers
  186. A representation for derangement numbers in terms of a tridiagonal determinant
  187. {Some integral inequalities of Hermite--Hadamard type for $s$-geometrically convex functions
  188. A closed form for the Stirling polynomials in terms of the Stirling numbers
  189. An explicit formula for derivative polynomials of the tangent function
  190. The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function
  191. Some properties of the divided difference of psi and polygamma functions
  192. On an Analogue of Euler Polynomials and Related to Extended Fermionic p-Adic Integrals on $$ {\mathbb{Z}}_{p} $$ ...
  193. Some Inequalities of the Bell Polynomials
  194. Some Inequalities of the Bell Polynomials
  195. Some inequalities for the Bell numbers
  196. Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations
  197. Integral Representations of the Catalan Numbers and Their Applications
  198. Integral representations of bivariate complex geometric mean and their applications
  199. Simplifying differential equations concerning degenerate Bernoulli and Euler numbers
  200. Alternative proofs for summation formulas of some trigonometric series
  201. Some explicit and recursive formulas of the large and little Schröder numbers
  202. Explicit formulas and recurrence relations for higher order Eulerian polynomials
  203. Some properties of central Delannoy numbers
  204. Explicit Formulas for Special Values of the Bell Polynomials of the Second Kind and for the Euler Numbers and Polynomials
  205. Closed forms for derangement numbers in terms of the Hessenberg determinants
  206. Integral inequalities of the Hermite--Hadamard type for (alpha,m)-GA-convex functions
  207. Expansions of the exponential and the logarithm of power series and applications
  208. Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body
  209. Notes on a Family of Inhomogeneous Linear Ordinary Differential Equations
  210. Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
  211. Two Nice Determinantal Expressions and A Recurrence Relation for the Apostol--Bernoulli Polynomials
  212. Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers
  213. A criterion to justify a holomorphic function
  214. Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers
  215. Simplifying Two Families of Nonlinear Ordinary DifferentialEquations
  216. Lévy–Khintchine Representation of Toader–Qi Mean
  217. A Closed Form for the Stirling Polynomials in Terms of the Stirling Numbers
  218. Several Series Identities Involving the Catalan Numbers
  219. Certain integrals involving the generalized hypergeometric function and the Laguerre polynomials
  220. Two explicit formulas for the generalized Motzkin numbers
  221. Hermite--Hadamard type inequalities for (alpha,m)-HA and strongly (alpha,m)-HA convex functions
  222. Integral inequalities of extended Simpson type for (alpha,m)-varepsilon-convex functions
  223. Bounding the gamma function in terms of the trigonometric and exponential functions
  224. SEVERAL FORMULAS FOR SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND AND APPLICATIONS
  225. Parametric integrals, the Catalan numbers, and the beta function
  226. Some new inequalities of the Hermite���Hadamard type for extended ((s1,m1)-(s2,m2))-convex functions on co-ordinates
  227. An explicit formula for Bernoulli polynomials in terms of $\boldsymbol r$-Stirling numbers of the second kind
  228. Some properties of the Schröder numbers
  229. Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations
  230. Some Properties of the Hermite Polynomials and Their Squares and Generating Functions
  231. Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
  232. A double inequality for an integral mean in terms of the exponential and logarithmic means
  233. An Improper Integral with a Square Root
  234. Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
  235. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials
  236. Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants
  237. Some Integral Transforms of the Generalized k-Mittag-Leffler Function
  238. The reciprocal of the weighted geometric mean is a Stieltjes function
  239. A recovery of two determinantal representations for derangement numbers
  240. A determinantal representation for derangement numbers
  241. Some properties of the Catalan–Qi function related to the Catalan numbers
  242. Some new and explicit identities related with the Appell-type degenerate q-Changhee polynomials
  243. The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform
  244. Some Properties of a Function Originating from Geometric Probability for Pairs of Hyperplanes Intersecting with a Convex Body
  245. Properties and inequalities for the (h1, h2)- and (h1, h2, m)-GA-convex functions
  246. Three Identities of the Catalan-Qi Numbers
  247. Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers
  248. SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
  249. Hermite–Hadamard type inequalities for n-times differentiable and geometrically quasi-convex functions
  250. On the Appell type λ -Changhee polynomials
  251. Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function
  252. The harmonic and geometric means are Bernstein functions
  253. Two closed forms for the Bernoulli polynomials
  254. Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions
  255. Bounds for the Ratio of Two Gamma Functions: from Gautschi’s and Kershaw’s Inequalities to Complete Monotonicity
  256. On some Hermite–Hadamard type inequalities for (s, QC)-convex functions
  257. A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean
  258. Complete monotonicity of divided differences of the di- and tri-gamma functions with applications
  259. Logarithmically complete monotonicity of a function related to the Catalan-Qi function
  260. An inequality involving the gamma and digamma functions
  261. Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind
  262. Integral representations and properties of some functions involving the logarithmic function
  263. Schur-convexity of the Catalan–Qi function
  264. Sharp inequalities for bounding Seiffert mean in terms of the arithmetic, centroidal, and contra-harmonic means
  265. Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers
  266. SOME NEW INTEGRAL INEQUALITIES OF HERMITE{HADAMARD TYPE FOR (α, m; P)-CONVEX FUNCTIONS ON CO-ORDINATES
  267. INTEGRAL INEQUALITIES OF HERMITE-HADAMARD TYPE FOR ((α;m); log)-CONVEX FUNCTIONS ON CO-ORDINATES
  268. An Explicit Formula for the Bell Numbers in Terms of the Lah and Stirling Numbers
  269. Some inequalities for the trigamma function in terms of the digamma function
  270. Hermite-Hadamard Type Inequalities for the Product of $(\alpha, m)$-Convex Function
  271. Derivatives of tangent function and tangent numbers
  272. Some new Hermite���Hadamard type inequalities for differentiable co-ordinated convex functions
  273. REMARKS ON COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE GAMMA FUNCTION
  274. Some new Hermite--Hadamard type inequalities for geometrically quasi-convex functions on co-ordinates
  275. A logarithmically completely monotonic function involving the gamma function and originating from the Catalan numbers and function
  276. Hermite–Hadamard-Type Integral Inequalities for Functions Whose First Derivatives are Convex
  277. An integral representation of the Catalan numbers
  278. Several closed expressions for the Euler numbers
  279. An integral representation, some inequalities, and complete monotonicity of the Bernoulli numbers
  280. Logarithmically complete monotonicity of a power-exponential function involving the logarithmic and psi functions
  281. Explicit expressions for a family of the Bell polynomials and applications
  282. Integral inequalities of Hermite���Hadamard type for logarithmically h-preinvex functions
  283. Some best approximation formulas and inequalities for the Wallis ratio
  284. Symmetry identities of q-Bernoulli polynomials of the second kind
  285. Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function
  286. Sharp bounds for the Neuman-Sándor mean in terms of the power and contraharmonic means
  287. Pólya type integral inequalities: Origin, variants, proofs, refinements, generalizations, equivalences, and applications
  288. On Schur m-power convexity for ratios of some means
  289. A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind
  290. Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
  291. The additivity of polygamma functions
  292. A note on three variable symmetric identities for modified q-Bernoulli polynomials arising from bosonic p-adic integral on Zp
  293. A note on three variable symmetric identities for q-Euler polynomials arising from fermionic p-adic integral on Zp
  294. Sharp Inequalities for Polygamma Functions
  295. Some inequalities of Hermite-Hadamard type for m-harmonic-arithmetically convex functions
  296. A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS
  297. A class of completely monotonic functions involving the gamma and polygamma functions
  298. Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
  299. Hermite-Hadamard type inequalities for geometricallyr-convex functions
  300. Inequalities of Hermite–Hadamard type involving an s-convex function with applications
  301. An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind
  302. A double inequality for bounding Toader mean by the centroidal mean
  303. Integral representations and complete monotonicity related to the remainder of Burnside’s formula for the gamma function
  304. Some inequalities of Qi type for double integrals
  305. Complete monotonicity of a function involving the gamma function and applications
  306. Sharp bounds for Neuman-Sándor’s mean in terms of the root-mean-square
  307. Complete monotonicity of functions involving the $q$-trigamma and $q$-tetragamma functions
  308. An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions
  309. Some Integral Inequalities of Hermite-Hadamard Type for Functions Whose n-times Derivatives are (α,m)-Convex
  310. On the degree of the weighted geometric mean as a complete Bernstein function
  311. Refinements and Sharpening of some Huygens and Wilker Type Inequalities
  312. Some Hermite–Hadamard type inequalities for geometrically quasi-convex functions
  313. Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
  314. Some Inequalities for the Generalized Trigonometric and Hyperbolic Functions
  315. Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions
  316. Absolute monotonicity of a function involving the exponential function
  317. Complete monotonicity of a function involving the p-psi function and alternative proofs
  318. COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS
  319. Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
  320. Some new inequalities of Simpson type for strongly $$\varvec{s}$$ s -convex functions
  321. Some inequalities of Hermite-Hadamard type for $r$-$\varphi$-preinvex functions
  322. Hermite-Hadamard Type Inequalities for (m, h1, h2)-Convex Functions Via Riemann-Liouville Fractional Integrals
  323. Some inequalities for ( h , m ) -convex functions
  324. Integral inequalities of Hermite-Hadamard type for functions whose derivatives are α-preinvex
  325. Hermite--Hadamard type inequalities for geometric-arithmetically $s$-convex functions
  326. Hermite-Hadamard type inequalities for n-times differentiable and preinvex functions
  327. Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
  328. Sharp inequalities for the psi function and harmonic numbers
  329. Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
  330. Some identities and an explicit formula for Bernoulli and Stirling numbers
  331. The Function (b x − a x )∕x: Ratio’s Properties
  332. Lévy-Khintchine representation of the geometric mean of many positive numbers and applications
  333. Schur-harmonic convexity for differences of some special means in two variables
  334. The best bounds for Toader mean in terms of the centroidal and arithmetic means
  335. A unified proof of several inequalities and some new inequalities involving Neuman-S\'andor mean
  336. An integral representation for the weighted geometric mean and its applications
  337. Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem
  338. Monotonicity results and inequalities for the inverse hyperbolic sine function
  339. Integral inequalities of Hermite-Hadamard type for functions whose third derivatives are convex
  340. Convexity of the generalized sine function and the generalized hyperbolic sine function
  341. Integral representations and properties of Stirling numbers of the first kind
  342. Some Integral Inequalities on Time Scales
  343. Lévy–Khintchine Representations of the Weighted Geometric Mean and the Logarithmic Mean
  344. A completely monotonic function involving the tri- and tetra-gamma functions
  345. Hermite–Hadamard type integral inequalities for geometric-arithmeticallys-convex functions
  346. Some inequalities for (s1;m1)-(s2;m2)-convex functions on the co-ordinates
  347. On proofs for monotonicity of a function involving the psi and exponential functions
  348. Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function
  349. Some exact constants for the approximation of the quantity in the Wallis’ formula
  350. Complete monotonicity of a function involving the divided difference of digamma functions
  351. COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS
  352. Some Hermite-Hadamard type inequalities for functions whose n-th derivatives are (α, m)-convex
  353. Inequalities of Hermite-Hadamard type for convex functions which are n-times differentiable
  354. Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions
  355. Some Hermite–Hadamard type inequalities for log-h-convex functions
  356. Some integral inequalities of Simpson type for GA-ɛ-convex functions
  357. Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
  358. Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities
  359. Convergence, monotonicity, and inequalities of sequences involving continued powers
  360. Some Inequalities for Multiple Integrals on then-Dimensional Ellipsoid, Spherical Shell, and Ball
  361. Some Hermite-Hadamard type inequalities for n-time differentiable "Equation missing" -convex functions
  362. Schur-harmonic convexity for differences of some means
  363. Some new integral inequalities
  364. Some properties of a class of functions related to completely monotonic functions
  365. Complete monotonicity of two functions involving the tri-and tetra-gamma functions
  366. Monotonicity of functions connected with the gamma function and the volume of the unit ball
  367. Refinements of lower bounds for polygamma functions
  368. A class of logarithmically completely monotonic functions related to the gamma function with applications
  369. Some new inequalities of Hermite–Hadamard type forn-time differentiable functions which arem-convex
  370. Generalizations of Hermite–Hadamard inequality ton-time differentiable functions which ares-convex in the second sense
  371. A completely monotonic function involving the tri-gamma function and with degree one
  372. Monotonicity and logarithmic convexity relating to the volume of the unit ball
  373. A refinement of a double inequality for the gamma function
  374. Sharpening and generalizations of Shafer's inequality for the arc sine function
  375. Hermite–Hadamard type inequalities for the m- and (α, m)-geometrically convex functions
  376. Bounds for the ratio of two gamma functions---From Wendel's and related inequalities to logarithmically completely monotonic functions
  377. Complete monotonicity of a function involving the ratio of gamma functions and applications
  378. Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>P</i>-Convex
  379. On Integral Inequalities of Hermite‐Hadamard Type for s‐Geometrically Convex Functions
  380. Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means
  381. Some sharp inequalities involving Seiffert and other means and their concise proofs
  382. Logarithmic convexity of Gini means
  383. A simple proof of Oppenheim's double inequality relating to the cosine and sine functions
  384. Several integral inequalities on time scales
  385. Sharp bounds for harmonic numbers
  386. An extension of an inequality for ratios of gamma functions
  387. A class of completely monotonic functions involving divided differences of the polygamma functions
  388. An alternative proof of Elezović-Giordano-Pečarić's theorem
  389. The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values
  390. Some bounds for the complete elliptic integrals of the first and second kinds
  391. Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions
  392. Some logarithmically completely monotonic functions related to the gamma function
  393. A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE GAMMA FUNCTION
  394. Some properties of extended remainder of binet’s first formula for logarithm of gamma function
  395. Generalizations of some classical inequalities via a special functional property
  396. Complete monotonicity of some functions involving polygamma functions
  397. Some properties of functions related to the gamma and psi functions
  398. Two new proofs of the complete monotonicity of a function involving the psi function
  399. Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic
  400. Bounds for the Ratio of Two Gamma Functions
  401. Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
  402. Properties and applications of a function involving exponential functions
  403. A class of logarithmically completely monotonic functions associated with the gamma function
  404. A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi–Kershaw’s inequality
  405. Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values
  406. A simple proof of logarithmic convexity of extended mean values
  407. Several q-integral inequalities
  408. Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems
  409. Sharpening and Generalizations of Shafer's Inequality for the Arc Tangent Function
  410. Wendel’s and Gautschi’s inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions
  411. A new upper bound in the second Kershaw's double inequality and its generalizations
  412. A generalization of van der Corput’s inequality
  413. Monotonicity and logarithmic concavity of two functions involving exponential function
  414. Darboux’s formula with integral remainder of functions with two independent variables
  415. A new lower bound in the second Kershaw's double inequality
  416. Alternative proofs for inequalities of some trigonometric functions
  417. Supplements to a class of logarithmically completely monotonic functions associated with the gamma function
  418. FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION
  419. A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality
  420. A class ofk-log-convex functions and their applications to some special functions
  421. A general refinement of Jordan's inequality and a refinement of L. Yang's inequality
  422. SOME COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND POLYGAMMA FUNCTIONS
  423. Refinements, extensions and generalizations of the second Kershaw's double inequality
  424. A new refinement of Young's inequality
  425. New Generalizations of an Integral Inequality
  426. Some integral inequalities on time scales
  427. A function involving gamma function and having logarithmically absolute convexity
  428. Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic
  429. Sums of series of Rogers dilogarithm functions
  430. A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality
  431. Three classes of logarithmically completely monotonic functions involving gamma and psi functions
  432. Monotonicity result for generalized logarithmic means
  433. Logarithmically completely monotonic functions concerning gamma and digamma functions
  434. A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums
  435. LOGARITHMIC CONVEXITY OF THE ONE-PARAMETER MEAN VALUES
  436. Complete monotonicity of the logarithmic mean
  437. Some New Bounds for Mathieu's Series
  438. On a new generalization of Martins' inequality
  439. Monotonicity of ratio between the generalized logarithmic means
  440. A mononotonicity result of a function involving the gamma function
  441. More notes on a functional equation
  442. Logarithmically completely monotonic functions relating to the gamma function
  443. Two logarithmically completely monotonic functions connected with gamma function
  444. 90.41 Introducing the Dirac delta function
  445. Monotonicity Properties and Inequalities of Functions Related to Means
  446. Note on Alzer's inequality
  447. Some completely monotonic functions involving the gamma and polygamma functions
  448. Monotonicity of sequences involving convex function and sequence
  449. Monotonicity of sequences involving geometric means of positive sequences with monotonicity and logarithmical convexity
  450. The best bounds in Gautschi-Kershaw inequalities
  451. An extension and a refinement of van der Corput′s inequality
  452. An alternative note on the Schur-convexity of the extended mean values
  453. Some completely monotonic functions involving polygamma functions and an application
  454. A Note on Schur-Convexity of Extended Mean Values
  455. Generalization of an inequality of Alzer for negative powers
  456. NOTES ON THE SCHUR-CONVEXITY OF THE EXTENDED MEAN VALUES
  457. Some New Iyengar Type Inequalities
  458. Extension of an Inequality of H. Alzer for Negative Powers
  459. The best bounds in Wallis' inequality
  460. Generalization and Refinements of Hermite-Hadamard's Inequality
  461. Notes on double inequalities of Mathieu′s series
  462. Note on weighted Carleman-type inequality
  463. A complete monotonicity property of the gamma function
  464. Some notes on a functional equation
  465. A lower bound for ratio of power means
  466. Inequalities of some trigonometric functions
  467. AN INEQUALITY BETWEEN RATIO OF THE EXTENDED LOGARITHMIC MEANS AND RATIO OF THE EXPONENTIAL MEANS
  468. INEQUALITIES AND MONOTONICITY FOR THE RATIO OF GAMMA FUNCTIONS
  469. On a Generalization of Martins' Inequality
  470. On new proofs of Wilker's inequalities involving trigonometric functions
  471. Generalizations of Bernoulli numbers and polynomials
  472. Inequalities involving the sequence ∛(a + ∛(a+...+ ∛(a)))
  473. Generalizations of Euler numbers and polynomials
  474. Some new Steffensen pairs
  475. Estimates of an integral in terms of the $L^p$-norm of the $(n+1)$st derivative of its integrand
  476. Monotonicity of sequences involving convex and concave functions
  477. Inequalities and monotonicity of the ratio of the geometric means of a positive arithmetic sequence with unit difference
  478. On Steffensen pairs
  479. Logarithmic convexity of extended mean values
  480. Generalization of Bernoulli polynomials
  481. An inductive proof for an identity involving (n k) and the partial sums of some series
  482. Monotonicity results and inequalities for the gamma and incomplete gamma functions
  483. Evaluation of a class of definite integrals
  484. Inequalities for Generalized Weighted Mean Values of Convex Function
  485. Inequalities for a Weighted Multiple Integral
  486. New proofs of weighted power mean inequalities and monotonicity for generalized weighted mean values
  487. On a new generalization of Alzer's inequality
  488. Generalization of H. Alzer's Inequality
  489. Note on monotonicity of generalized weighted mean values
  490. Inequalities for the Incomplete Gamma and Related Functions
  491. Inequalities for a multiple integral
  492. Recursion Formulae for $\sum^n_{m=1} m^k$
  493. Some Inequalities of the Incomplete Gamma and Related Functions
  494. A new proof of monotonicity for extended mean values
  495. Some inequalities constructed by Tchebysheff's integral inequality
  496. The function $(b^x-a^x)/x$: inequalities and properties
  497. Refinements and Extensions of an Inequality, III
  498. Generalized weighted mean values with two parameters
  499. A Simple Proof of Monotonicity for Extended Mean Values
  500. Refinements and Extensions of an Inequality, II
  501. 80.22 Inequalities for an Integral