The asymptotics of a generalised Struve function

Abstract

A generalised Struve function has recently been introduced by Ali, Mondal and Nisar [J. Korean Math. Soc. {\bf 54} (2017) 575--598] as \[(\frac{1}{2} z)^{ν+1}\sum_{n=0}^\infty\frac{(\frac{1}{2} z)^{2n}}{Γ(n+\frac{3}{2}) Γ(an+ν+\frac{3}{2})},\] 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.

arXiv comment14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1711.03006, arXiv:1708.04824