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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 for the direct function itself





http://functions.wolfram.com/07.12.26.0008.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 3, 2 z + 1] == (-(Sin[Pi \[Nu]]/2)) Csc[Pi \[Mu]] E^(Pi I \[Mu]) (((z + 1)^(\[Mu]/2)/z^(\[Mu]/2)) MeijerG[{{\[Nu] + 1, -\[Nu]}, {}}, {{0}, {\[Mu]}}, z] - (z^(\[Mu]/2)/(z + 1)^(\[Mu]/2)) Pochhammer[\[Nu] - \[Mu] + 1, 2 \[Mu]] MeijerG[{{\[Nu] + 1, -\[Nu]}, {}}, {{0}, {-\[Mu]}}, z]) /; !Element[\[Nu], Integers] && !Element[\[Mu], Integers]










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", ",", RowBox[List[RowBox[List["2", " ", "z_"]], "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Mu]"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List["\[Mu]", "/", "2"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", "\[Mu]", "}"]]]], "}"]], ",", "z"]], "]"]]]], SuperscriptBox["z", RowBox[List["\[Mu]", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["\[Mu]", "/", "2"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["\[Nu]", "-", "\[Mu]", "+", "1"]], ",", RowBox[List["2", " ", "\[Mu]"]]]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "\[Mu]"]], "}"]]]], "}"]], ",", "z"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List["\[Mu]", "/", "2"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]], "&&", RowBox[List["!", RowBox[List["\[Mu]", "\[Element]", "Integers"]]]]]]]]]]]]










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





2001-10-29





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