Triple convolution identities on Bernoulli polynomials and Euler polynomials

被引:0
|
作者
Wang, Weiping [1 ]
Liu, Hongmei [2 ]
Jia, Cangzhi [3 ]
机构
[1] Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
[2] Dalian Nationalities Univ, Sch Sci, Dalian 116600, Peoples R China
[3] Dalian Maritime Univ, Dept Math, Dalian 116026, Peoples R China
基金
中国国家自然科学基金;
关键词
Bernoulli polynomials; Euler polynomials; Combinatorial identities; Sums of products; Triple convolutions; PRODUCTS; SUMS; NUMBERS;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, by means of the generating function method, we establish 38 triple convolution identities on the Bernoulli polynomials and the Euler polynomials (i.e., sums of products of three Bernoulli polynomials or Euler polynomials), which have the form Sigma(i+j+k=ni,j,k >= 0) lambda(i)mu(j) n!/i!j!k! Fi+alpha(x)/(i+1)alpha G(j+beta)(y)/(j+1)beta Hk+gamma(z)/(k+1)gamma, where alpha, beta, gamma is an element of N-0, lambda, mu is an element of C, and F-k(x), G(k)(y), H-k(z) are the Bernoulli polynomials or the Euler polynomials. As supplements, we also give 3 quadruple convolution identities on the Bernoulli and Euler polynomials and 4 triple convolution identities on the Bernoulli and Euler numbers.
引用
收藏
页码:369 / 395
页数:27
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