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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 > Classical cases for powers of Legendre Q





http://functions.wolfram.com/07.12.26.0030.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 3, Sqrt[z + 1]]^2 == ((Sqrt[Pi] E^(2 Pi I \[Mu]) Gamma[1 + \[Mu] + \[Nu]])/ (2 Gamma[1 - \[Mu] + \[Nu]])) MeijerG[{{-\[Nu]}, {1/2, \[Nu] + 1}}, {{0, \[Mu], -\[Mu]}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]








Standard Form





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MathML Form







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Rule Form





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


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





2001-10-29