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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 involving algebraic functions





http://functions.wolfram.com/07.12.26.0011.01









  


  










Input Form





(1 + z)^(\[Mu]/2) LegendreQ[\[Nu], \[Mu], 3, 2/z + 1] == ((E^(Pi \[Mu] I) Gamma[1 + \[Mu] + \[Nu]])/(2 Gamma[1 - \[Mu] + \[Nu]])) MeijerG[{{1, 1 + \[Mu]}, {}}, {{1 + \[Nu]}, {-\[Nu]}}, 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", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z_"]], ")"]], FractionBox["\[Mu]_", "2"]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", RowBox[List[FractionBox["2", "z_"], "+", "1"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[Mu]", " ", "\[ImaginaryI]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", "\[Mu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "+", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List["-", "\[Nu]"]], "}"]]]], "}"]], ",", "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





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