# User:Tohline/Math/EQ Toroidal01

 $~ Q_\nu[t t^' - (t^2-1)^{1 / 2} (t^{'2} - 1)^{1 / 2} \cos\psi]$ $~=$ $~ Q_\nu(t) P_\nu(t^') + 2\sum_{n=1}^\infty (-1)^n Q^n_\nu(t) P^{-n}_\nu(t^') \cos(n\psi)$ A. Erdélyi (1953):  Volume I, §3.11, p. 169, eq. (4)
 Valid for: $~t, t^'$  real $~1 < t^' < t$ $~\nu \ne -1, -2, -3,$ … $~\psi$   real