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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/07.09.07.0001.01









  


  










Input Form





LegendreP[\[Nu], \[Mu], 3, z] == ((2^(\[Mu] - 2 \[Nu])/((-1)^\[Nu] (Gamma[-\[Mu] - \[Nu]] Gamma[\[Nu] + 1]))) ((z + 1)^(\[Mu]/2)/(z - 1)^(\[Mu]/2)) Integrate[((t - 1)^\[Nu]/(t + 1)^(\[Mu] + \[Nu] + 1)) (t - (z + 3)/(z - 1))^\[Nu], {t, -1, 1}])/(1/(1 - z))^\[Nu] /; -1 < Re[\[Nu]] < -Re[\[Mu]]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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