Paper Info
Title
Some Difference Equations for Srivastava's λ-Generalized Hurwitz-Lerch Zeta Functions with Applications.
Abstract
In this article, we establish some new difference equations for the family of lambda-generalized Hurwitz-Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions. Several authors investigated such functions and their analytic properties, but no work has been reported for an estimation of their values. We perform some numerical computations to evaluate these functions for different values of the involved parameters. It is shown that the direct evaluation of involved integrals is not possible for the large values of parameter s; nevertheless, using our new difference equations, we can evaluate these functions for the large values of s. It is worth mentioning that for the small values of this parameter, our results are 100% accurate with the directly computed results using their integral representation. Difference equations so obtained are also useful for the computation of some new integrals of products of lambda-generalized Hurwitz-Lerch zeta functions and verified to be consistent with the existing results. A derivative property of Mellin transforms proved fundamental to present this investigation.
Year
DOI
Venue
2019
10.3390/sym11030311
SYMMETRY-BASEL
Keywords
Field
DocType
analytic number theory,lambda-generalized Hurwitz-Lerch zeta functions,derivative properties,recurrence relations,integral representations,Mellin transform
Mellin transform,Applied mathematics,Recurrence relation,Mathematical analysis,Integral representation,Analytic number theory,Mathematics,Computation
Journal
Volume
Issue
Citations 
11
3
0
PageRank 
References 
Authors
0.34
5
1
Name
Order
Citations
PageRank
Asifa Tassaddiq143.46