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 LegendreP

 http://functions.wolfram.com/05.03.23.0001.01

 Input Form

 Sum[Cos[k ArcCos[z]] LegendreP[n - k, z], {k, 1, n}] == n LegendreP[n, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List[RowBox[List["Cos", "[", RowBox[List["k", " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", "z"]], "]"]]]]]], "\[Equal]", RowBox[List["n", " ", RowBox[List["LegendreP", "[", RowBox[List["n", ",", "z"]], "]"]]]]]]]]

 MathML Form

 k = 1 n cos ( k cos - 1 ( z ) ) P TagBox["P", LegendreP] n - k ( z ) n P TagBox["P", LegendreP] n ( z ) k 1 n k z LegendreP n -1 k z n LegendreP n z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], RowBox[List[RowBox[List["Cos", "[", RowBox[List["k_", " ", RowBox[List["ArcCos", "[", "z_", "]"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["n_", "-", "k_"]], ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["n", " ", RowBox[List["LegendreP", "[", RowBox[List["n", ",", "z"]], "]"]]]]]]]]

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

 2001-10-29