Sums of products of Bernoulli numbers
type: Item
instance of: scholarly article
title: Sums of products of Bernoulli numbers
zbMATH Open document ID: 0863.11011
author: Karl Dilcher
published in: Journal of Number Theory
publication date: 1996-10-14T00:00:00Z
review text: Closed expressions are obtained for sums of products of Bernoulli numbers of the form \[ \sum {{2n} \choose {2j_1,\dots,2j_N}} B_{2j_1}\cdots B_{2j_N}, \] where the factor in parentheses is a multinomial coefficient and the summation is extended over all nonnegative integers \(j_1,\dots,j_N\) whose sum is \(n\). Corresponding results are derived for Bernoulli polynomials, and for Euler numbers and polynomials. Sums of this type were previously studied by Euler for \(n=2\), and by others for \(n=3\) and 4.
Mathematics Subject Classification ID: 11B68
zbMATH DE Number: 934965
zbMATH Keywords: Euler polynomials
zbMATH Keywords: sums of products of Bernoulli numbers
zbMATH Keywords: Bernoulli polynomials
zbMATH Keywords: Euler numbers
reviewed by: Tom M. Apostol
MaRDI profile type: Publication
full work available at URL: jnth.1996.0110
OpenAlex ID: W2093823995
DOI: 10.1006/JNTH.1996.0110
description: scientific article; zbMATH DE number 934965