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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions





http://functions.wolfram.com/05.03.26.0006.01









  


  








Input Form





(z + 1)^(-1 - n) LegendreP[n, (z - 1)/(z + 1)] == (1/Gamma[n + 1]^2) MeijerG[{{-n}, {-n}}, {{0, 0}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], RowBox[List["LegendreP", "[", RowBox[List["n", ",", FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List["n", "+", "1"]], "]"]], "2"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["-", "n"]], "}"]], ",", RowBox[List["{", RowBox[List["-", "n"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "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





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





2001-10-29