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~
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

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