Recurrence relation for Struve function (2)
From specialfunctionswiki
Theorem
The following formula holds: $$\mathbf{H}_{\nu-1}(z)-\mathbf{H}_{\nu+1}(z) = 2\mathbf{H}_{\nu}'(z) - \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\frac{3}{2})},$$ 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): $12.1.10$
