Template:Math/EQ Toroidal01

	$Q_{\nu }[t{t}^{\text{'}}-(t^2-1{)}^{1/2}(t^{\text{'}2}-1{)}^{1/2}\cos \psi ]$	$=$	$Q_{\nu }(t)P_{\nu }(t^{\text{'}})+2\sum _{n=1}^{\mathrm{\infty }}(-1{)}^n{Q}_{\nu }^n(t)P_{\nu }^{-n}(t^{\text{'}})\cos (n\psi )$
A. Erdélyi (1953):  Volume I, §3.11, p. 169, eq. (4)

Valid for:

$t,t^{\text{'}}$  real

$1<t^{\text{'}}<t$

$\nu \ne -1,-2,-3,$ …

$\psi$   real