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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F~1





http://functions.wolfram.com/07.07.26.0040.01









  


  










Input Form





LegendreP[\[Nu], z] == (-((2^(-3 - \[Nu]) (1 - Cos[2 Pi \[Nu]]) Sec[Pi \[Nu]])/Sqrt[Pi])) (((-Gamma[1 + \[Nu]]) (Csc[(Pi \[Nu])/2] + (Sqrt[-z^2]/z) Sec[(Pi \[Nu])/2]) Hypergeometric2F1Regularized[(1 + \[Nu])/2, (2 + \[Nu])/2, 3/2 + \[Nu], 1/z^2])/(z (-z^2)^(\[Nu]/2)) + 2^(1 + 2 \[Nu]) Gamma[-\[Nu]] (-z^2)^(\[Nu]/2) (Csc[(Pi \[Nu])/2] - (Sqrt[-z^2]/z) Sec[(Pi \[Nu])/2]) Hypergeometric2F1Regularized[ -(\[Nu]/2), (1 - \[Nu])/2, 1/2 - \[Nu], 1/z^2]) /; !IntervalMemberQ[Interval[{-1, 0}], z]










Standard Form





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MathML Form







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</mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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