General Convolution Identities for Bernoulli and Euler Polynomials

2015/07/20 by K. Dilcher, Dilcher, K., C. Vignat +1
Mathematics · #11B68 - 60E05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B68 #msc:60E05

paper · pdf · doi:10.48550/arxiv.1507.05356

20 pages

arxiv created 2015/07/20 · arxiv updated 2015/07/21

Abstract

Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k ≥ 2) convolution identities for Bernoulli and Euler polynomials. This is achieved by use of an elementary result on uniformly distributed random variables. These identities depend on k positive real parameters, and as special cases we obtain numerous known and new identities for these polynomials. In particular we show that the well-known identities of Miki and Matiyasevich for Bernoulli numbers are special cases of the same general formula.

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