Modified Struve Function

$${\mathcal L}_\nu(z) = ({\textstyle{1\over 2}}z)^{\nu+1} \sum_{k=0}^\infty {({\textstyle... ...{2k}\over \Gamma(k+{\textstyle{3\over 2}})\Gamma(k+\nu+{\textstyle{3\over 2}})}$$

$$= {2({\textstyle{1\over 2}}z)^\nu\over \sqrt{\pi}\,\Gamma(\nu+{\textstyle{1\over 2}})} \int_0^{\pi/2} \sinh(z\cos\theta)\sin^{2\nu}\theta\,d\theta,$$

where $\Gamma(z)$ is the Gamma Function.

See also Anger Function, Struve Function, Weber Functions

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Modified Struve Function ${\bf L}_\nu(x)$.'' §12.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 498, 1972.