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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 algebraic functions





http://functions.wolfram.com/07.11.26.0017.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 2, 1/Sqrt[z + 1]]/(1 + z)^((\[Nu] + 1)/2) == (Sqrt[Pi]/(2^(-\[Nu] + 1) Gamma[1 - \[Mu] + \[Nu]])) MeijerG[{{-(\[Nu]/2), (1 - \[Nu])/2}, {(1 + \[Mu])/2}}, {{\[Mu]/2, -(\[Mu]/2)}, {(1 + \[Mu])/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", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z_"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Nu]_", "+", "1"]], ")"]]]]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", FractionBox["1", SqrtBox[RowBox[List["z_", "+", "1"]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "+", "\[Mu]"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Mu]", "2"], ",", RowBox[List["-", FractionBox["\[Mu]", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "+", "\[Mu]"]], "2"], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "+", "1"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], "]"]]]]], "/;", 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