A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials

Kucukoglu I., ŞİMŞEK Y., Srivastava H. M.

QUAESTIONES MATHEMATICAE, vol.42, no.4, pp.465-478, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.2989/16073606.2018.1459925
  • Journal Name: QUAESTIONES MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.465-478
  • Keywords: Bernoulli numbers and Bernoulli polynomials, Euler numbers and Euler polynomials, Riemann and Hurwitz (or generalized) zeta functions, Hurwitz-Lerch zeta function, Lerch zeta function, polylogarithm function, multiplication formula, functional equation, Mellin transformation, UNIFIED PRESENTATION, EULER POLYNOMIALS, GENERATING-FUNCTIONS, Q-EXTENSIONS, BERNOULLI, (H, SUMS
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to investigate some classes of higher-order Apostol-type numbers and Apostol-type polynomials. We construct Lerch-type zeta functions which interpolate these numbers and polynomials at negative integers. Moreover, by combining some well-known identities such as the Chu-Vandermonde identity with the Lerch-type zeta functions and generating functions for the higher- order Apostol-type numbers and Apostol-type polynomials, we derive some relations and identities including functional equation for these Lerch-type zeta functions with other zeta type functions, Raabe-type multiplication formula for the higher-order Apostol-type polynomials and the Stirling numbers. Finally, we give some remarks and observations on Lerch-type zeta functions and their functional equations.