## E421 -- Evolutio formulae integralis $$\int x^{f-1} dx\, (lx)^{m/n}$$ integratione a valore $$x = 0$$ ad $$x = 1$$ extensa

(Solution of a formula for the integral $$\int x^{f-1} dx\, (lx)^{m/n}$$, the integration being extended from the value $$x = 0$$ to $$x = 1$$)

Summary:

According to the records, it was presented to the St. Petersburg Academy on July 4, 1771.

Publication:
• Originally published in Novi Commentarii academiae scientiarum Petropolitanae 16, 1772, pp. 91-139
• Opera Omnia: Series 1, Volume 17, pp. 316 - 357
• Reprinted in Institutiones calculi integralis 4, 1794, pp. 78-121 [E421a]; ed. tertia 4, 1845, pp. 78- 121 [E421b]
Documents Available:
• Original publication: E421
• English draft translation (Alexander Aycock): E421
• 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 E421 include:
• Dutka J., “The early history of the factorial function.” Archive for History of Exact Sciences, 43 (3), pp. 225-249 (1991).