Struve Function - Definitions - Power Series Expansion

Power Series Expansion

Struve functions, denoted as have the following power series form

\mathbf{H}_\alpha(x) = \sum_{m=0}^\infty \frac{(-1)^m}{\Gamma(m+\frac{3}{2}) \Gamma(m+\alpha+\frac{3}{2})} {\left({\frac{x}{2}}\right)}^{2m+\alpha+1}

where is the gamma function.

The modified Struve function, denoted as have the following power series form

\mathbf{L}_{\nu}(z) = {\left({\frac{z}{2}}\right)}^{\nu+1} \sum_{k=0}^\infty \frac{1}{\Gamma(\frac{3}{2}+k) \Gamma(\frac{3}{2}+k+\nu)} {\left({\frac{z}{2}}\right)}^{2k}

Read more about this topic:  Struve Function, Definitions

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