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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 algebraic functions





http://functions.wolfram.com/07.12.26.0055.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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


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





2001-10-29