E736 -- De summatione serierum in hac forma contentarum a/1 + (a^2)/4 + (a^3)/9 + (a^4)/16 + (a^5)/25 + (a^6/36) + etc.

E736 -- De summatione serierum in hac forma contentarum a/1 + a²/4 + a³/9 + a⁴/16 + a⁵/25 + a⁶/36 + etc.

(On the summation of series contained in the form a/1 + a²/4 + a³/9 + a⁴/16 + a⁵/25 + a⁶/36 + etc.)

Summary:

Euler calls the function f(a) and splits it into two parts, an odd part and an even part, then evaluates f(1/2).

Publication:

Originally published in Memoires de l'academie des sciences de St.-Petersbourg 3, 1811, pp. 26-42
Opera Omnia: Series 1, Volume 16, pp. 117 - 138

Documents Available:

Original publication: E736
Ian Bruce has made a translation of E736 available at his web page, Mathematical Works of the 17th Century.
German translation (Artur Diener and Alexander Aycock): E736

Return to the Euler Archive

E736 -- De summatione serierum in hac forma contentarum a/1 + a2/4 + a3/9 + a4/16 + a5/25 + a6/36 + etc.

E736 -- De summatione serierum in hac forma contentarum a/1 + a²/4 + a³/9 + a⁴/16 + a⁵/25 + a⁶/36 + etc.