Difference between revisions of "Relationship between Struve function and hypergeometric pFq"

Theorem: The following formula holds: $$H_{\nu}(z)=\dfrac{2(\frac{z}{2})^{\nu+1}}{\sqrt{\pi}\Gamma(\nu+\frac{3}{2})} {}_1F_2 \left( 1; \dfrac{3}{2}+\nu,\dfrac{3}{2};-\dfrac{z^2}{4} \right),$$ where $\mathbf{H}_{\nu}$ denotes a Struve function, $\pi$ denotes pi, $\Gamma$ denotes the gamma function, and ${}_2F_1$ denotes the hypergeometric pFq.