SOME REMARKS ON THE GENERALIZED APOSTOL-BERNOULLI AND APOSTOL-EULER POLYNOMIALS


Boutiche M. A., KARGIN L., Rahmani M.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, vol.50, no.4, pp.1133-1145, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1007/s13226-019-0380-1
  • Journal Name: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1133-1145
  • Keywords: Apostol-Bernoulli polynomials, Apostol-Euler polynomials, Hurwitz-Lerch-Zeta functions, recurrence relations, stirling numbers, WEIGHTED STIRLING NUMBERS, LERCH ZETA-FUNCTIONS, UNIFIED PRESENTATION, IDENTITIES, FAMILIES, 1ST
  • Akdeniz University Affiliated: Yes

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.