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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Representations through more general functions > Through Meijer G > Generalized cases involving Legendre Q





http://functions.wolfram.com/07.09.26.0072.01









  


  








Input Form





LegendreP[\[Mu] - 1/2, \[Nu] + 1/2, 3, Sqrt[1 + z^2]/z] LegendreQ[\[Nu], \[Mu], 3, Sqrt[z^2 + 1]] == ((E^(Pi I \[Mu]) Cos[Pi \[Mu]] Gamma[1 + \[Mu] + \[Nu]])/(Pi Sqrt[2])) MeijerG[{{3/4}, {5/4 + \[Nu], 1/4 - \[Nu]}}, {{1/4, 1/4 + \[Mu], 1/4 - \[Mu]}, {}}, z, 1/2] /; Re[z] > 0








Standard Form





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MathML Form







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</mi> <mi> &#956; </mi> </msubsup> <mo> ( </mo> <semantics> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <annotation encoding='Mathematica'> TagBox[SqrtBox[RowBox[List[SuperscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;+&quot;, &quot;1&quot;]]], HoldComplete[LegendreQ, 3]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </mfrac> <mo> &#8290; 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Rule Form





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





2001-10-29