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

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

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