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Convolution and Reciprocity Formulas for Bernoulli Polynomials

Takashi Agoh / Karl Dilcher
Published Online: 2011-08-04 | DOI: https://doi.org/10.1515/INTEG.2011.067


We prove a new convolution identity for sums of products of two Bernoulli polynomials. This can be rewritten to obtain a reciprocity relation for a related sum. The proof uses some results on Stirling numbers of both kinds which are of independent interest. In particular, a class of polynomials related to the Stirling numbers of the second kind turns out to be a useful tool.

Keywords.: Bernoulli Numbers; Bernoulli Polynomials; Stirling Numbers; Convolutions; Reciprocity Relations

About the article

Received: 2010-10-07

Accepted: 2011-05-18

Published Online: 2011-08-04

Published in Print: 2011-12-01

Citation Information: Integers, Volume 11, Issue 6, Pages 849–861, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2011.067.

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