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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Representations through more general functions > Through Meijer G > Classical cases involving unit step theta





http://functions.wolfram.com/07.09.26.0024.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z_"]], ")"]], RowBox[List["-", "\[Mu]_"]]], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List["2", " ", SqrtBox["z_"]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "\[Mu]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Mu]", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "-", "\[Mu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], SqrtBox["\[Pi]"]], "/;", 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