Some remarks on the generalized Apostol-Bernoulli and Apostol-Euler polynomials

Mohamed Amine Boutiche (), Levent Kargin () and Mourad Rahmani ()
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Mohamed Amine Boutiche: USTHB, Faculty of Mathematics
Levent Kargin: Akdeniz University
Mourad Rahmani: USTHB, Faculty of Mathematics

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 4, 1133-1145

Abstract: Abstract In this paper, we give explicit expressions for generalized Apostol-Bernoulli and Apostol-Euler polynomials. As consequences, we deduce some explicit representations for other Apostol-type polynomials. Moreover, we find an algorithm based on a three-term recurrence for the calculation of generalized Apostol-Euler numbers and polynomials. As an application, we derive a formula for the values of some kinds of Hurwitz-Lerch Zeta functions at negative arguments.

Keywords: Apostol-Bernoulli polynomials; Apostol-Euler polynomials; Hurwitz-Lerch-Zeta functions; recurrence relations; stirling numbers (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0380-1

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