# A FURTHER GENERALIZATION OF APOSTOL-BERNOULLI POLYNOMIALS AND RELATED POLYNOMIALS

• Tremblay, R. (Department of Mathematics and Computer Science, University of Quebec at Chicoutimi) ;
• Gaboury, S. (Department of Mathematics and Computer Science, University of Quebec at Chicoutimi) ;
• Fugere, J. (Department of Mathematics and Computer Science, Royal Military College)
• Accepted : 2012.06.11
• Published : 2012.09.25

#### Abstract

The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition 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 extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

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#### Cited by

1. -Extensions for the Apostol Type Polynomials vol.2018, pp.1687-0409, 2018, https://doi.org/10.1155/2018/2937950