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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > Series representations > Generalized power series > Expansions at z==infinity





http://functions.wolfram.com/07.12.06.0031.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 3, z] == (-((2^(-\[Nu] - 1) E^(I Pi \[Mu]) Cos[Pi \[Nu]])/Sqrt[Pi])) Gamma[-(1/2) - \[Nu]] Gamma[1 + \[Mu] + \[Nu]] (z - 1)^(-\[Mu]/2 - \[Nu] - 1) (z + 1)^(\[Mu]/2) Hypergeometric2F1[1 + \[Nu], 1 + \[Mu] + \[Nu], 2 (1 + \[Nu]), 2/(1 - z)] /; !IntervalMemberQ[Interval[{-1, 1}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Mu]"]]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["\[Mu]", "2"]]], "-", "\[Nu]", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List["\[Mu]", "/", "2"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], ",", RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]]]], ",", FractionBox["2", RowBox[List["1", "-", "z"]]]]], "]"]]]], SqrtBox["\[Pi]"]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29





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