This paper extends tools developed by Richard Crandall in [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet L-series and character polylogarithms.

A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation. Identities are generated involving both elementary and special functions. Infinite sums of special functions include those of the gamma and polygamma functions, the Hurwitz Zeta function, the polygamma function, th...

ABSTRACT Motivated essentially by recent works by several authors (see, for example, Bin-Saad [Math J Okayama Univ 49:37-52, 2007] and Katsurada [Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13-25, 1997], the main objective in this paper is to present a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associa...

The current study is fully devoted to studying differential subordination and superordination theorems of analytic functions with some sandwich results involving linear operators Iλs,a,μ. This operator was obtained by the Hadamard product family integral Hurwitlz-Lerch Zeta function. demonstrate possibility capability extracting Sandwich theorem, conclusion includes superordination.