LegendreP[\[Nu], \[Mu], 2, z] == ((Sin[Pi \[Nu]]/(Pi Gamma[-\[Mu] - \[Nu]] Gamma[1 - \[Mu] + \[Nu]])) (x + 1)^((1/2) \[Mu]) Exp[Pi I \[Mu] Floor[Arg[z - x]/(2 Pi)]] ((-2 Pi^2 I Floor[Arg[-x + z]/(2 Pi)] Csc[Pi \[Nu]] Hypergeometric2F1Regularized[-\[Nu], 1 + \[Nu], 1 + \[Mu], (1 + x)/2])/ E^(I Pi \[Mu] Floor[Arg[-x + z]/(2 Pi)]) - MeijerG[{{1 + \[Nu], -\[Nu]}, {}}, {{0, -\[Mu]}, {}}, (1 + x)/2]/ E^(2 I Pi \[Mu] Floor[Arg[-x + z]/(2 Pi)]) + ((1/(2 (-1 + x^2))) (2 Pi^2 I E^(I Pi \[Mu] Floor[Arg[-x + z]/(2 Pi)]) Floor[Arg[-x + z]/(2 Pi)] Csc[Pi \[Nu]] ((-1 + x^2) \[Nu] Hypergeometric2F1Regularized[1 - \[Nu], 2 + \[Nu], 2 + \[Mu], (1 + x)/2] + 2 \[Mu] (1 + \[Nu]) Hypergeometric2F1Regularized[-\[Nu], 1 + \[Nu], 1 + \[Mu], (1 + x)/2]) + (-1 + x^2) MeijerG[{{\[Nu], -1 - \[Nu]}, {}}, {{0, -1 - \[Mu]}, {}}, (1 + x)/2] + 2 \[Mu] MeijerG[{{1 + \[Nu], -\[Nu]}, {}}, {{0, -\[Mu]}, {}}, (1 + x)/2]) (z - x))/E^(2 I Pi \[Mu] Floor[Arg[-x + z]/(2 Pi)]) + \[Ellipsis]))/(1 - x)^((1/2) \[Mu]) /; (z -> x) && Element[x, Reals] && x < -1

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2007-05-02