D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1)

Theorem

The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \left[ z^{-\nu}\mathbf{H}_{\nu}(z) \right] = \dfrac{1}{\sqrt{\pi}2^{\nu}\Gamma(\nu+\frac{3}{2})} - z^{-\nu}\mathbf{H}_{\nu+1}(z),$$ where $\mathbf{H}$ denotes a Struve function.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.13$