E321 -- Observationes circa integralia formularum \( \int x^{p-1} dx \, (1-x^n)^{q/n-1} \) posito post integrationem \(x = 1\)
(Observations concerning the integrals of formulas \( \int x^{p-1} dx \, (1-x^n)^{q/n-1} \) setting \(x = 1\) after integration)
Summary:
Publication:
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Originally published in Melanges de philosophie et de la mathematique de la societe royale de Turin 3, 1766, pp. 156-177
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Opera Omnia: Series 1, Volume 17, pp. 268 - 288
Documents Available:
- Original publication (the Euler Archive would like to thank the Acadmey
of Sciences of Torino for these images):
E321
- Alexander Aycock has made draft translations into German and English, available online at Euler-Kreis Mainz.
- 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 E321 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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