Higher-order convolutions for Bernoulli and Euler polynomials

被引：17

作者：

Agoh, Takashi ^{[1
]}

Dilcher, Karl ^{[2
]}

机构：

[1] Tokyo Univ Sci, Dept Math, Noda, Chiba 2788510, Japan

[2] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 4R2, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 419卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Bernoulli polynomials; Euler polynomials; Bernoulli numbers; Euler numbers; Genocchi numbers; Convolution identities; NUMBERS; IDENTITIES;

D O I：

10.1016/j.jmaa.2014.05.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove convolution identities of arbitrary orders for Bernoulli and Euler polynomials, i.e., sums of products of a fixed but arbitrary number of these polynomials. They differ from the more usual convolutions found in the literature by not having multinomial coefficients as factors. This generalizes a special type of convolution identity for Bernoulli numbers which was first discovered by Yu. Matiyasevich. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1235 / 1247

页数：13

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