Does an analog of the following formula $$ P_{\nu}\left(z_1 z_2 - \sqrt{z_1^2-1}\sqrt{z_2^2-1}\cos\psi\right) = {1\over 2\pi} \int^{\pi}_{-\pi} {\left( z_1 + \sqrt{z_1^2-1}\cos(x-\psi) \right)^{\nu} \over \left( z_2 + \sqrt{z_2^2-1}\cos(x) \right)^{\nu+1}} \, dx $$ exist for the function $Q_{\nu}\left(z_1 z_2 - \sqrt{z_1^2-1}\sqrt{z_2^2-1}\cos\psi\right)$? I've searched in every reference I can remember but I can't find anything. A result with $\psi =0$ would be enough as well. Thanks!
2026-03-27 19:53:15.1774641195
Integral representation of Legendre function of the second kind
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