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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/07.12.06.0030.01









  


  










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) Sum[((Pochhammer[1 + \[Nu], k] Pochhammer[1 + \[Mu] + \[Nu], k])/ (Pochhammer[2 (1 + \[Nu]), k] k!)) (2/(1 - z))^k, {k, 0, Infinity}] /; Abs[(1 - z)/2] > 1










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[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], ",", "k"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", RowBox[List["1", "-", "z"]]], ")"]], "k"]]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]]]], ",", "k"]], "]"]], " ", RowBox[List["k", "!"]]]]]]]]], SqrtBox["\[Pi]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", FractionBox[RowBox[List["1", "-", "z"]], "2"], "]"]], ">", "1"]]]]]]]]










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





2001-10-29





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