A succinct method for investigating the sums of infinite series through differential formulae

Details A succinct method for investigating the sums of infinite series through differential formulae A succinct method for investigating the sums of infinite series through differential formulae

2007-05-05

arxiv.org/abs/0705.0768v1

Mathematics

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8 pages

Scientific paper

Translation of "Methodus succincta summas serierum infinitarum per formulas differentiales investigandi" (1780). Euler wants to represent some given series of functions S(x)=X(x)+X(x+1)+X(x+2)+etc. in a different way. He writes S as a series in derivatives of X with unknown coefficients. He makes a generating function V(z) out of these coefficients, which is the same as a generating function that involves the Bernoulli numbers.

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