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 LegendreP

 http://functions.wolfram.com/05.03.07.0001.01

 Input Form

 LegendreP[n, z] == (1/Pi) Integrate[(z - Sqrt[z^2 - 1] Cos[t])^n, {t, 0, Pi}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["\[Pi]", " "]]], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], " ", RowBox[List["Cos", "[", "t", "]"]]]]]], ")"]], "n"], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]

 MathML Form

 P TagBox["P", LegendreP] n ( z ) 1 π 0 π ( z - z 2 - 1 cos ( t ) ) n t LegendreP n z 1 -1 t 0 z -1 z 2 -1 1 2 t n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LegendreP", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Pi]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], " ", RowBox[List["Cos", "[", "t", "]"]]]]]], ")"]], "n"], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Pi]"]]]]]

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

 2001-10-29