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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 involving sgn





http://functions.wolfram.com/07.12.26.0029.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 3, (1 + z)/(2 Sqrt[z])]/(Sign[1 - Abs[z]] (1 - z))^ \[Mu] == E^(Pi I \[Mu]) Sqrt[Pi] Gamma[1/2 - \[Mu]] MeijerG[{{(1 - \[Nu])/2 - \[Mu]}, {1 + \[Nu]/2 - \[Mu]}}, {{(\[Nu] + 1)/2}, {-(\[Nu]/2)}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Sign", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z", "]"]]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "3", ",", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["2", " ", SqrtBox["z"]]]]]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "\[Mu]"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "\[Mu]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "-", "\[Mu]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", FractionBox["\[Nu]", "2"], "-", "\[Mu]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Sign", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", "z_"]], ")"]]]], ")"]], RowBox[List["-", "\[Mu]_"]]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List["2", " ", SqrtBox["z_"]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "\[Mu]"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "\[Mu]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "-", "\[Mu]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", FractionBox["\[Nu]", "2"], "-", "\[Mu]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29





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