What is it about?
It is shown that the Beta integral that Euler calculated in 1730, Mengoli had already calculated in 1659, for natural numbers, and in 1672 for semi-integer numbers, by another path of exploration.
Featured Image
Why is it important?
The main result of this article is to show these calculations with their symbolic language and to analyze how Mengoli, through the definitions and theorems that he develops, shows the relationship between the values of the integrals and the exponents of the integrated algebraic expression. Our findings provide us with a new vision of Mengoli's ideas on the algorithmic calculus of quadratures, placing him as a pioneer in the integral calculus of the 17th century.
Perspectives
Currently, unpublished or recently published manuscripts of Leibniz are being investigated, since, in them, Leibniz commented on these Mengoli's works. This relationship will allow us to know the circulation of mathematical knowledge in XVIIth century in Europe.
Sra Mª Rosa Massa-Esteve
Universitat Politecnica de Catalunya
Read the Original
This page is a summary of: Euler’s beta integral in Pietro Mengoli’s works, Granular Matter, March 2009, Springer Science + Business Media,
DOI: 10.1007/s00407-009-0042-5.
You can read the full text:
Contributors
The following have contributed to this page
