The asymptotics of a generalised Struve function

TL;DR

This paper derives asymptotic expansions for a generalized Struve function with a real parameter for large complex arguments, extending previous definitions and providing numerical validation of the results.

Contribution

It provides the first asymptotic analysis of the generalized Struve function for large complex arguments with a real parameter a>-1.

Findings

Asymptotic expansions derived for large |z|

Numerical examples confirm the accuracy of the asymptotic formulas

Extension of the generalized Struve function analysis to real parameter a>-1

Abstract

A generalised Struve function has recently been introduced by Ali, Mondal and Nisar [J. Korean Math. Soc. {\bf 54} (2017) 575--598] as \[(\frac{1}{2} z)^{\nu+1}\sum_{n=0}^\infty\frac{(\frac{1}{2} z)^{2n}}{\Gamma(n+\frac{3}{2}) \Gamma(an+\nu+\frac{3}{2})},\] where $a$ is a positive integer. In this paper, we obtain the asymptotic expansions of this function for large complex $z$ when $a$ is a real parameter satisfying $a>-1$. Some numerical examples are presented to confirm the accuracy of the expansions.