Difference between revisions of "Relationship between Struve function and hypergeometric pFq"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\mathbf{H}_{\nu}(z)=\dfrac{2(\frac{z}{2})^{\nu+1}}{\sqrt{\pi}\Gamma(\nu+\frac{3}{2})} {}_1F_2 \left( 1; \dfrac{3}{2}+\nu,\dfrac{3}{2};-\dfrac{z^2}{4} \right),$$ | $$\mathbf{H}_{\nu}(z)=\dfrac{2(\frac{z}{2})^{\nu+1}}{\sqrt{\pi}\Gamma(\nu+\frac{3}{2})} {}_1F_2 \left( 1; \dfrac{3}{2}+\nu,\dfrac{3}{2};-\dfrac{z^2}{4} \right),$$ | ||
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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| − | + | ==Proof== | |
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| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 13:18, 25 June 2016
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.
