D/dz(z^(nu)H (nu))=z^(nu)H (nu-1)

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Theorem

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