The asymptotics of the Struve function ${\bf H}_\nu(z)$ for large complex order and argument

Abstract

We re-examine the asymptotic expansion of the Struve function ${\bf H}_\nu(z)$ for large complex values of $\nu$ and $z$ satisfying $|\arg\,\nu|\leq\pi/2$ and $|\arg\,z|<\pi/2$. Watson's analysis covers only the case of $\nu$ and $z$ of the same phase with $\nu/z$ in the intervals $(0,1)$ and $(1,\infty)$. The domains in the complex $\nu/z$-plane where the expansion takes on different forms are obtained.