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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.12.26.0072.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["\[Mu]_", "-", FractionBox["1", "2"]]], ",", RowBox[List["\[Nu]_", "+", FractionBox["1", "2"]]], ",", "3", ",", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]]]], "]"]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", FractionBox[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]], "z_"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "\[Mu]"]]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Mu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", RowBox[List[FractionBox["3", "4"], "-", "\[Mu]"]], ",", RowBox[List[FractionBox["3", "4"], "+", "\[Mu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "4"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], "-", "\[Nu]"]], ",", RowBox[List[FractionBox["3", "4"], "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["\[Pi]", " ", SqrtBox["2"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]










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





2001-10-29





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