Recurrence relation for Struve function (2)

From specialfunctionswiki
Revision as of 16:27, 4 November 2017 by Tom (talk | contribs) (Created page with "==Theorem== The following formula holds: $$\mathbf{H}_{\nu-1}(z)-\mathbf{H}_{\nu+1}(z) = 2\mathbf{H}_{\nu}'(z) - \dfrac{z^{\nu}}{2^{\nu}\sqrt{\pi}\Gamma(\nu+\frac{3}{2})},$$ w...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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