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

R. B. Paris

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arXiv · 1510.05110

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

R. B. Paris

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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.

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R. B. Paris. 2015-10-17. The asymptotics of the Struve function ${\bf H}_\nu(z)$ for large complex order and argument. https://arxiv.org/abs/1510.05110

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