An algorithm for computing mixed sums of products of Bernoulli polynomials and Euler polynomials. (January 2015)

• Record Type: Journal Article
• Authors: Feng, Lei; Wang, Weiping
• Is Part Of: Journal of symbolic computation. Volume 66(2015)
• Page Start: 84
• Page End: 97
• Publication Date: 2015-01
• Subjects: Bernoulli polynomials -- Euler polynomials -- Generating functions -- Partial fraction decompositions -- Sums of products; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.01.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, by the methods of partial fraction decomposition and generating function, we give an algorithm for computing mixed sums of products of l Bernoulli polynomials and k − l Euler polynomials, which are of the form T n, k λ ( y ; l, k − l ) : = ∑ j 1 + ⋯ + j k = n j 1, …, j k ⩾ 0 ∏ i = 1 k λ i j i ( n j 1, …, j k ) ∏ p = 1 l B j p ( x p ) ∏ q = l + 1 k E j q ( x q ), where λ = ( λ 1, …, λ k ), and λ 1, …, λ k are nonzero rational numbers. Moreover, some special sums are presented as examples.