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Modified Struve Function

$\displaystyle {\mathcal L}_\nu(z)$ $\textstyle =$ $\displaystyle ({\textstyle{1\over 2}}z)^{\nu+1} \sum_{k=0}^\infty {({\textstyle...
...{2k}\over \Gamma(k+{\textstyle{3\over 2}})\Gamma(k+\nu+{\textstyle{3\over 2}})}$  
  $\textstyle =$ $\displaystyle {2({\textstyle{1\over 2}}z)^\nu\over \sqrt{\pi}\,\Gamma(\nu+{\textstyle{1\over 2}})} \int_0^{\pi/2} \sinh(z\cos\theta)\sin^{2\nu}\theta\,d\theta,$  

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

See also Anger Function, Struve Function, Weber Functions


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.

© 1996-9 Eric W. Weisstein