Difference between revisions of "Recurrence relation for Struve fuction"
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(Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\nu-1}(z)+\mathbf{H}_{\nu+1}(z) = \dfrac{2\nu}{z} \mathbf{H}_{\nu}(z) + \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\fra...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral representation of Struve function (3)|next=}}: $12.1.9$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral representation of Struve function (3)|next=Recurrence relation for Struve function (2)}}: $12.1.9$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 16:26, 4 November 2017
Theorem
The following formula holds: $$\mathbf{H}_{\nu-1}(z)+\mathbf{H}_{\nu+1}(z) = \dfrac{2\nu}{z} \mathbf{H}_{\nu}(z) + \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\frac{3}{2})},$$ where $\mathbf{H}$ denotes the Struve function, $\pi$ denotes pi, and $\Gamma$ denotes the gamma function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.9$
