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A Further Generalization of Apostol-Bernoulli Polynomials and Related polynomials
( R Trem Blay ),( S Gab Oury ),( J Fug Ere ) 호남수학회 2012 호남수학학술지 Vol.34 No.3
The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the de nition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an ex- tension and some analogues of the Srivastava-Pinter addition theorem [28] for both classes. Finally, by making use of the new addition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.