2007/05/05 by Leonhard Euler, Euler, Leonhard
Mathematics · #01A50 #65B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #math.CA #math.HO #msc:01A50 #msc:65B15
paper · pdf · doi:10.48550/arxiv.0705.0768
8 pages
arxiv created 2007/05/05 · openalex publication_date 2007/05/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.