Heine's identity

In mathematical analysis, Heine's identity, named after Heinrich Eduard Heine{{cite book \frac{1}{\sqrt{z-\cos\psi}} = \frac{\sqrt{2}}{\pi}\sum_{m=-\infty}^\infty Q_{m-\frac12}(z) e^{im\psi} where Q_{m-\frac12} is a Legendre function of the second kind, which has degree, m − , a half-integer, and argument, z, real and greater than one. This expression can be generalized{{cite conference | book-title = 3D Stellar Evolution, ASP Conference Proceedings, held 22-26 July 2002 at University of California Davis, Livermore, California, USA. Edited by Sylvain Turcotte, Stefan C. Keller and Robert M. Cavallo (z-\cos\psi)^{n-\frac12} = \sqrt{\frac{2}{\pi}}\frac{(z^2-1)^{\frac{n}{2}}}{\Gamma(\frac12-n)} \sum_{m=-\infty}^{\infty} \frac{\Gamma(m-n+\frac12)}{\Gamma(m+n+\frac12)}Q_{m-\frac12}^n(z)e^{im\psi}, where \scriptstyle,\Gamma is the Gamma function.

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