Template:Math/EQ Toroidal05

	$\underset{a}{\overset{b}{\int }}[(\nu -\sigma )(\nu +\sigma +1)+({\rho }^2-{\mu }^2)(1-z^2{)}^{-1}]w_{\nu }^{\mu }{w}_{\sigma }^{\rho }dz$	$=$	$[z(\nu -\sigma )w_{\nu }^{\mu }{w}_{\sigma }^{\rho }+(\sigma +\rho )w_{\nu }^{\mu }{w}_{\sigma -1}^{\rho }-(\nu +\mu )w_{\nu -1}^{\mu }{w}_{\sigma }^{\rho }{]}_a^b$
A. Erdélyi (1953):  Volume I, §3.12, p. 169, eq. (1)

where, $w_{\nu }^{\mu }(z)$ and $w_{\sigma }^{\rho }(z)$ denote any solutions of Legendre's differential equation