Difference between revisions of "D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1)"
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(Created page with "==Theorem== The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \left[ z^{-\nu}\mathbf{H}_{\nu}(z) \right] = \dfrac{1}{\sqrt{\pi}2^{\nu}\Gamma(\nu+\frac{3}{2})} - z...") |
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Latest revision as of 00:55, 21 December 2017
Theorem
The following formula holds: $$\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.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.13$
