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

We re-examine the asymptotic expansion of the Struve function ${\bf H}_\nu(z)$forlargecomplexvaluesof$\nu$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 $\nu \mathrm{/}z$ in the intervals $(0,1)$ and $(1,\mathrm{\infty })$. The domains in the complex $\nu \mathrm{/}z$-plane where the expansion takes on different forms are obtained.