Difference between revisions of "Relationship between Struve function and hypergeometric pFq"
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<strong>[[Relationship between Struve function and hypergeometric pFq|Theorem]]:</strong> The following formula holds: | <strong>[[Relationship between Struve function and hypergeometric pFq|Theorem]]:</strong> The following formula holds: | ||
| − | $$ | + | $$\mathbf{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),$$ |
where $\mathbf{H}_{\nu}$ denotes a [[Struve function]], $\pi$ denotes [[pi]], $\Gamma$ denotes the [[gamma function]], and ${}_2F_1$ denotes the [[hypergeometric pFq]]. | where $\mathbf{H}_{\nu}$ denotes a [[Struve function]], $\pi$ denotes [[pi]], $\Gamma$ denotes the [[gamma function]], and ${}_2F_1$ denotes the [[hypergeometric pFq]]. | ||
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Revision as of 18:40, 28 June 2015
Theorem: The following formula holds: $$\mathbf{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.
Proof: █
