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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 hypergeometric functions > Involving 2F1





http://functions.wolfram.com/07.09.26.0086.01









  


  








Input Form





LegendreP[\[Nu], \[Mu], 3, z] == (2^\[Mu] Sqrt[Pi] ((-((2 z)/(Gamma[(1/2) (-\[Mu] - \[Nu])] Gamma[(1/2) (1 - \[Mu] + \[Nu])]))) Hypergeometric2F1[ (1/2) (1 - \[Mu] - \[Nu]), (1/2) (2 - \[Mu] + \[Nu]), 3/2, z^2] + (1/(Gamma[(1/2) (1 - \[Mu] - \[Nu])] Gamma[(1/2) (2 - \[Mu] + \[Nu])])) Hypergeometric2F1[(1/2) (1 - \[Mu] + \[Nu]), (-(1/2)) (\[Mu] + \[Nu]), 1/2, z^2]))/((z - 1)^(\[Mu]/2) (z + 1)^(\[Mu]/2))








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", "\[Mu]"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List["-", FractionBox["\[Mu]", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List["-", FractionBox["\[Mu]", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "z"]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "-", "\[Nu]"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "-", "\[Mu]", "+", "\[Nu]"]], ")"]]]], ",", FractionBox["3", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Mu]"]], "-", "\[Nu]"]], ")"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], ")"]]]], "]"]]]]]]], "+", FractionBox[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], ")"]]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Mu]", "+", "\[Nu]"]], ")"]]]], ",", FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "-", "\[Nu]"]], ")"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "-", "\[Mu]", "+", "\[Nu]"]], ")"]]]], "]"]]]]]]], ")"]]]]]]]]


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





2007-05-02