Küçükoğlu, İremŞimşek, YılmazSrivastava, H. M.2024-08-202024-08-2020191607-36061727-933X10.2989/16073606.2018.14599252-s2.0-85051965293https://doi.org/10.2989/16073606.2018.1459925https://hdl.handle.net/20.500.14591/122The 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.eninfo:eu-repo/semantics/closedAccessBernoulli numbers and Bernoulli polynomialsEuler numbers and Euler polynomialsRiemann and Hurwitz (or generalized) zeta functionsHurwitz-Lerch zeta functionLerch zeta functionpolylogarithm functionmultiplication formulafunctional equationMellin transformationArticle4784Q246542WOS:000466387500004Q2