Template:Math/EQ Toroidal03

	$Q_{\nu }^{\mu }(z)$	$=$	$e^{i\mu \pi }(2\pi {)}^{-\frac{1}{2}}(z^2-1{)}^{\mu /2}\mathrm{\Gamma }(\mu +\frac{1}{2})\{\underset{0}{\overset{\pi }{\int }}(z-\cos t{)}^{-\mu -\frac{1}{2}}\cos [(\nu +\frac{1}{2})t]dt-\cos (\nu \pi )\underset{0}{\overset{\mathrm{\infty }}{\int }}(z+\cosh t{)}^{-\mu -\frac{1}{2}}{e}^{-(\nu +\frac{1}{2})t}dt\}$
A. Erdélyi (1953):  Volume I, §3.7, p. 156, eq. (10)

Valid for:

$\mathrm{R}\mathrm{e}\nu >-\frac{1}{2}$

and

$\mathrm{R}\mathrm{e}(\nu +\mu +1)>0.$