A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
NATL INQUIRY SERVICES CENTRE PTY LTD
Access Rights
info:eu-repo/semantics/closedAccess
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.
Description
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
Journal or Series
Quaestiones Mathematicae
WoS Q Value
Q2
Scopus Q Value
Q2
Volume
42
Issue
4
