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 LegendreP

 http://functions.wolfram.com/05.07.03.0008.01

 Input Form

 LegendreP[n, -n, 2, z] == (1/(2^n Gamma[n + 1])) (1 - z^2)^(n/2)

 Standard Form

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

 MathML Form

 P TagBox["P", LegendreP] n - n ( z TagBox["z", HoldComplete[LegendreP, 2]] ) 2 - n Γ ( n + 1 ) ( 1 - z 2 ) n / 2 LegendreP n -1 n 2 z 2 -1 n Gamma n 1 -1 1 -1 z 2 n 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreP", "[", RowBox[List["n_", ",", RowBox[List["-", "n_"]], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["n", "/", "2"]]]]], RowBox[List["Gamma", "[", RowBox[List["n", "+", "1"]], "]"]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.