E816 -- Considerations sur quelques formules integrales dont les valeurs peuvent etre exprimees, en certains cas, par la quadrature du cercle

(Thoughts on certain integral formulas for which the values can be expressed under certain circumstances by the squaring of ther circle)

Summary:

This paper is concerned with several families of definite integrals of rational functions, which, upon integration, have values expressible purely in terms of trigonometric functions.

Publication:

Originally published in Opera Postuma 1, 1862, pp. 408-438
Opera Omnia: Series 1, Volume 19, pp. 439 - 490
Reprinted in Bullet. d. sc. mathem. 42, 1880, pp. 207-256; p. 207: “Mémoire de Léonard Euler publié conformément au manuscrit autographe; par M. Charles Henry” [E816a]
The handwritten version is found in the National Library in Paris.

Documents Available:

Original publication: E816
English draft translation (Eric Proffitt): E816
The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E816 include:
- Dutka J., “The early history of the factorial function.” Archive for History of Exact Sciences, 43 (3), pp. 225-249 (1991).

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