All Stories

  1. On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function
  2. Several identities and relations related to q-analogues of Pochhammer k-symbol with applications to Fuss–Catalan–Qi numbers
  3. Monotonicity, convexity, and Maclaurin series expansion of Qi's normalized remainder of Maclaurin series expansion with relation to cosine
  4. Determinantal Expressions, Identities, Concavity, Maclaurin Power Series Expansions for van der Pol Numbers, Bernoulli Numbers, and Cotangent
  5. A Sufficient and Necessary Condition for the Power-Exponential Function 1+1xαx to Be a Bernstein Function and Related nth Derivatives
  6. Several integral inequalities of the Hermite-Hadamard type for s-(β, F)-convex functions
  7. Hermite–Hadamard type inequalities for harmonic-arithmetic extended $ (s_1, m_1) $-$ (s_2, m_2) $ coordinated convex functions
  8. Hermite–Hadamard’s Integral Inequalities of (α,s)-GA- and (α,s,m)-GA-Convex Functions
  9. Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean
  10. Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means
  11. Some new integral inequalities of the Simpson type for MT-convex functions
  12. 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
  13. Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities
  14. Generalizations of Hermite–Hadamard Type Integral Inequalities for Convex Functions
  15. Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios
  16. Direct, Inverse, and Equivalence Theorems for Weighted Szász—Durrmeyer—Bézier Operators in Orlicz Spaces
  17. Coordinated MT- s ...
  18. Some properties of the Hermite polynomials
  19. A ratio of finitely many gamma functions and its properties with applications
  20. Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions
  21. 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
  22. Determinantal Formulas and Recurrent Relations for Bi-Periodic Fibonacci and Lucas Polynomials
  23. Inequalities of Hermite-Hadamard type for extended harmonically (s,m)-convex functions
  24. Necessary and sufficient conditions on the Schur convexity of a bivariate mean
  25. Refinements of Young’s Integral Inequality via Fundamental Inequalities and Mean Value Theorems for Derivatives1
  26. Several Explicit and Recurrent Formulas for Determinants of Tridiagonal Matrices via Generalized Continued Fractions
  27. Retraction Note to: A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant
  28. From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
  29. Closed formulas and identities on the Bell polynomials and falling factorials
  30. Some properties and an application of multivariate exponential polynomials
  31. Correction: Monotonicity and inequalities related to complete elliptic integrals of the second kind
  32. Monotonicity and inequalities related to complete elliptic integrals of the second kind
  33. Several explicit and recursive formulas for generalized Motzkin numbers
  34. Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions
  35. On GT-convexity and related integral inequalities
  36. Relations among Bell polynomials, central factorial numbers, and central Bell polynomials
  37. Generalizations and applications of Young’s integral inequality by higher order derivatives
  38. Equivalent theorem of approximation by linear combination of weighted Baskakov–Kantorovich operators in Orlicz spaces
  39. A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant
  40. Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind
  41. Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind
  42. The inverse of a triangular matrix and several identities of the Catalan numbers
  43. On integral inequalities of Hermite-Hadamard type for coordinated r-mean convex functions
  44. Shannon Type Inequalities for Kapur’s Entropy
  45. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers
  46. On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function
  47. Integral Representations of the Large and Little Schröder Numbers
  48. Some identities for a sequence of unnamed polynomials connected with the Bell polynomials
  49. A diagonal recurrence relation for the Stirling numbers of the first kind
  50. Lévy-Khintchine representation of Toader-Qi mean
  51. Some identities related to Eulerian polynomials and involving the Stirling numbers
  52. A representation for derangement numbers in terms of a tridiagonal determinant
  53. A closed form for the Stirling polynomials in terms of the Stirling numbers
  54. An explicit formula for derivative polynomials of the tangent function
  55. Some Inequalities of the Hermite-Hadamard Type for Harmonically Quasi-Convex Functions
  56. The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function
  57. Some properties of the divided difference of psi and polygamma functions
  58. Generalizations of the Bell Numbers and Polynomials and Their Properties
  59. Some Identities for a Sequence of Unnamed Polynomials Connected with the Bell Polynomials
  60. Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations
  61. Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind
  62. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers
  63. Integral Representations of the Catalan Numbers and Their Applications
  64. Some Identities Relating to Eulerian Polynomials and Involving Stirling Numbers
  65. Simplifying differential equations concerning degenerate Bernoulli and Euler numbers
  66. Some explicit and recursive formulas of the large and little Schröder numbers
  67. Explicit formulas and recurrence relations for higher order Eulerian polynomials
  68. Some properties of central Delannoy numbers
  69. Explicit Formulas for Special Values of the Bell Polynomials of the Second Kind and for the Euler Numbers and Polynomials
  70. Closed forms for derangement numbers in terms of the Hessenberg determinants
  71. Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body
  72. Notes on a Family of Inhomogeneous Linear Ordinary Differential Equations
  73. Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers
  74. Closed Expressions of the Fibonacci Polynomials in Terms of Tridiagonal Determinants
  75. A criterion to justify a holomorphic function
  76. A Closed Form for the Stirling Polynomials in Terms of the Stirling Numbers
  77. Explicit and recursive formulas, integral representations, and properties of the large Schröder numbers
  78. An explicit formula for Bernoulli polynomials in terms of $\boldsymbol r$-Stirling numbers of the second kind
  79. Some properties of the Schröder numbers
  80. Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations
  81. Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
  82. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials
  83. The reciprocal of the weighted geometric mean is a Stieltjes function
  84. A recovery of two determinantal representations for derangement numbers
  85. The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform
  86. Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers
  87. SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
  88. Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function
  89. Some Generalizations of Integral Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions
  90. Complete monotonicity of divided differences of the di- and tri-gamma functions with applications
  91. Logarithmically complete monotonicity of a function related to the Catalan-Qi function
  92. An inequality involving the gamma and digamma functions
  93. REMARKS ON COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE GAMMA FUNCTION
  94. The additivity of polygamma functions
  95. Sharp Inequalities for Polygamma Functions
  96. A class of completely monotonic functions involving the gamma and polygamma functions
  97. Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
  98. On the degree of the weighted geometric mean as a complete Bernstein function
  99. Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
  100. Sharp inequalities for the psi function and harmonic numbers
  101. Some identities and an explicit formula for Bernoulli and Stirling numbers
  102. Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions
  103. Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives
  104. A Class of Logarithmically Completely Monotonic Functions and Their Applications
  105. Monotonicity results and inequalities for the inverse hyperbolic sine function
  106. Logarithmically completely monotonic functions and applications
  107. A completely monotonic function involving the tri- and tetra-gamma functions
  108. On proofs for monotonicity of a function involving the psi and exponential functions
  109. Complete monotonicity of a function involving the divided difference of digamma functions
  110. Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
  111. Some properties of completely monotonic sequences and related interpolation
  112. Complete monotonicity of two functions involving the tri-and tetra-gamma functions
  113. Monotonicity of functions connected with the gamma function and the volume of the unit ball
  114. Refinements of lower bounds for polygamma functions
  115. A completely monotonic function involving the tri-gamma function and with degree one
  116. Monotonicity and logarithmic convexity relating to the volume of the unit ball
  117. A refinement of a double inequality for the gamma function
  118. Sharpening and generalizations of Shafer's inequality for the arc sine function
  119. Complete monotonicity of a function involving the ratio of gamma functions and applications
  120. Logarithmic convexity of Gini means
  121. A simple proof of Oppenheim's double inequality relating to the cosine and sine functions
  122. Sharp bounds for harmonic numbers
  123. An extension of an inequality for ratios of gamma functions
  124. A class of completely monotonic functions involving divided differences of the polygamma functions
  125. An alternative proof of Elezović-Giordano-Pečarić's theorem
  126. The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values
  127. Some bounds for the complete elliptic integrals of the first and second kinds
  128. Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions
  129. Some logarithmically completely monotonic functions related to the gamma function
  130. A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE GAMMA FUNCTION
  131. Some properties of extended remainder of binet’s first formula for logarithm of gamma function
  132. Complete monotonicity of some functions involving polygamma functions
  133. Two new proofs of the complete monotonicity of a function involving the psi function
  134. Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic
  135. Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
  136. Properties and applications of a function involving exponential functions
  137. A simple proof of logarithmic convexity of extended mean values
  138. Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems
  139. Sharpening and Generalizations of Shafer's Inequality for the Arc Tangent Function
  140. Wendel’s and Gautschi’s inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions
  141. A class of logarithmically completely monotonic functions
  142. Monotonicity and logarithmic concavity of two functions involving exponential function
  143. Darboux’s formula with integral remainder of functions with two independent variables
  144. Alternative proofs for inequalities of some trigonometric functions
  145. A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality
  146. A class ofk-log-convex functions and their applications to some special functions
  147. A function involving gamma function and having logarithmically absolute convexity
  148. Some completely monotonic functions involving the gamma and polygamma functions
  149. Monotonicity of sequences involving convex function and sequence
  150. Monotonicity of sequences involving geometric means of positive sequences with monotonicity and logarithmical convexity
  151. The best bounds in Gautschi-Kershaw inequalities
  152. Some completely monotonic functions involving polygamma functions and an application
  153. Notes on double inequalities of Mathieu′s series
  154. Some notes on a functional equation
  155. A lower bound for ratio of power means
  156. AN INEQUALITY BETWEEN RATIO OF THE EXTENDED LOGARITHMIC MEANS AND RATIO OF THE EXPONENTIAL MEANS
  157. INEQUALITIES AND MONOTONICITY FOR THE RATIO OF GAMMA FUNCTIONS
  158. On new proofs of Wilker's inequalities involving trigonometric functions
  159. Generalizations of Bernoulli numbers and polynomials
  160. Estimates of an integral in terms of the $L^p$-norm of the $(n+1)$st derivative of its integrand
  161. On Steffensen pairs
  162. Generalization of Bernoulli polynomials
  163. An inductive proof for an identity involving (n k) and the partial sums of some series
  164. Inequalities for Generalized Weighted Mean Values of Convex Function