Some Relationships between the Generalized Apostol-Bernoulli and Apostol-Euler Polynomials

Burak Kurt^1,

¹Department of Mathematical Education, Faculty of Educations, Akdeniz University, TR-07058 Antalya, Turkey

Cite this paper:
Burak Kurt. Some Relationships between the Generalized Apostol-Bernoulli and Apostol-Euler Polynomials. Turkish Journal of Analysis and Number Theory. 2013; 1(1):54-58. doi: 10.12691/tjant-1-1-11

Abstract

The main objective of this paper is to introduce and investigate two new classes of generalized Apostol-Bernoulli polynomials B_n^[m-1,α^](x;c,α;λ) and Apostol-Euler polynomials ε_n^[m-1,α^](x;c,α;λ). In particular, we obtain addition formula for the new class of the generalized Apostol-Bernoulli polynomials. We also give some recurrence relations and Raabe relations for these polynomials.

Keywords:
Bernoulli polynomials and numbers Apostol-Bernoulli polynomials Apostol-Euler polynomials Generalized Apostol-Bernoulli polynomials

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