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.
%0 Generic
%1 citeulike:3036263
%A Euler, Leonhard
%D 2007
%K Vor1800 available-in-tex-format combinatorics mathematics pre1800
%T A succinct method for investigating the sums of infinite series through differential formulae
%U http://arxiv.org/abs/0705.0768
%X 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.
@misc{citeulike:3036263,
abstract = {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.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/232f1c7057f4e84815a6bb876990a0bcf/rwst},
citeulike-article-id = {3036263},
citeulike-linkout-0 = {http://arxiv.org/abs/0705.0768},
citeulike-linkout-1 = {http://arxiv.org/pdf/0705.0768},
description = {my bookmarks from citeulike},
eprint = {0705.0768},
interhash = {0585c92f71691a24b27b032fda9553df},
intrahash = {32f1c7057f4e84815a6bb876990a0bcf},
keywords = {Vor1800 available-in-tex-format combinatorics mathematics pre1800},
month = May,
posted-at = {2008-07-23 08:41:59},
priority = {2},
timestamp = {2009-08-18T18:29:35.000+0200},
title = {A succinct method for investigating the sums of infinite series through differential formulae},
url = {http://arxiv.org/abs/0705.0768},
year = 2007
}