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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.08.26.0016.01









  


  








Input Form





(UnitStep[1 - Abs[z]] LegendreP[\[Nu], \[Mu], 2, -1 + 2 z])/ (1 - z)^(\[Mu]/2) == MeijerG[{{}, {-\[Nu] - \[Mu]/2, 1 + \[Nu] - \[Mu]/2}}, {{-(\[Mu]/2), \[Mu]/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["-", FractionBox["\[Mu]_", "2"]]]], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "z_"]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", FractionBox["\[Mu]", "2"]]], ",", RowBox[List["1", "+", "\[Nu]", "-", FractionBox["\[Mu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Mu]", "2"]]], ",", FractionBox["\[Mu]", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "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