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

Abstract

We re-examine the asymptotic expansion of the Struve function ${\mathbf{H}}_{\nu }(z)$ for large complex values of $\nu$ and $z$ satisfying $|\arg \nu |\le \pi /2$ 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.

6 pages, 3 figures