A new class of generalized Apostol–Bernoulli polynomials and some analogues of the Srivastava–Pintér addition theorem

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• 作者：R. Tremblay^a ; ^{rtrembla@uqac.ca"" rel=""nofollow} ; S. Gaboury^b ; ^{s1gabour@uqac.ca"" rel=""nofollow} ; B.-J. Fugè ; re^b ; ^{fugerej@rmc.ca"" rel=""nofollow}
• 关键词：Generalized Bernoulli polynomials ; Generalized Euler polynomials ; Generalized Apostol&#x2013 ; Bernoulli polynomials ; Generalized Apostol&#x2013 ; Euler polynomials ; Stirling numbers of the second kind ; Generating functions
• 刊名：Applied Mathematics Letters
• 出版年：2011
• 出版时间：November 2011
• 年：2011
• 卷：24
• 期：11
• 页码：1888-1893
• 全文大小：225 K

文摘

The main purpose of this paper is to introduce and investigate a new class of generalized Apostol–Bernoulli polynomials based on a definition given by Natalini and Bernardini (2003) [22] for the generalized Bernoulli polynomials. We obtain a generalization of the Srivastava–Pintér addition theorem (Srivastava and Pintér (2004) [23]). We also give a list of expressions involving special functions that could be used to obtain some analogues of the Srivastava–Pintér addition theorem. Finally, we give an analogue featuring the new class of generalized Apostol–Bernoulli polynomials.