Recurrence relation for Struve fuction

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.9$