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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Representations through more general functions > Through Meijer G > Classical cases involving unit step theta





http://functions.wolfram.com/07.11.26.0020.01









  


  








Input Form





(UnitStep[Abs[z] - 1]/Sqrt[z - 1]) (LegendreQ[\[Nu], \[Mu], 2, -Sqrt[(z - 1)/z]] + LegendreQ[\[Nu], \[Mu], 2, Sqrt[(z - 1)/z]]) == (-((2^\[Mu] Pi^2 Tan[((\[Mu] + \[Nu])/2) Pi])/(Gamma[(1 - \[Mu] - \[Nu])/2] Gamma[1 + (\[Nu] - \[Mu])/2]))) MeijerG[{{(1 + \[Mu])/2, (1 - \[Mu])/2}, {}}, {{}, {(1 + \[Nu])/2, -(\[Nu]/2)}}, z] /; !Element[\[Nu], Integers] && !Element[\[Mu], Integers] && !IntervalMemberQ[Interval[{-Infinity, -1}], 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[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["Abs", "[", "z_", "]"]], "-", "1"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", RowBox[List["-", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], "z_"]]]]]], "]"]], "+", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], "z_"]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List["z_", "-", "1"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "\[Mu]"], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Tan", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Mu]", "+", "\[Nu]"]], ")"]], " ", "\[Pi]"]], "]"]]]], ")"]], " ", 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["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Mu]", "-", "\[Nu]"]], ")"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", FractionBox[RowBox[List["\[Nu]", "-", "\[Mu]"]], "2"]]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]], "&&", RowBox[List["!", RowBox[List["\[Mu]", "\[Element]", "Integers"]]]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]]]


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





2001-10-29