Difference between revisions of "User:Tohline/Math/EQ Toroidal03"

Latest revision as of 21:38, 1 July 2018

	<math>~Q_\nu^\mu(z)</math>	<math>~=</math>	<math>~ e^{i \mu \pi} ~ (2\pi)^{-\frac{1}{2}} (z^2-1)^{\mu/2} ~\Gamma(\mu + \tfrac{1}{2})~\biggl\{ \int_0^\pi (z - \cos t)^{-\mu - \frac{1}{2}} \cos[(\nu + \tfrac{1}{2})t] ~dt -\cos(\nu\pi) \int_0^\infty (z + \cosh t)^{-\mu - \frac{1}{2}} e^{-(\nu + \frac{1}{2})t} ~dt \biggr\} </math>
A. Erdélyi (1953): Volume I, §3.7, p. 156, eq. (10)

Valid for:

<math>~\mathrm{Re} ~\nu > -\tfrac{1}{2}</math>

and

<math>~\mathrm{Re} (\nu + \mu + 1) > 0 \, .</math>

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