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 LegendreP

 http://functions.wolfram.com/05.07.23.0001.01

 Input Form

 Sum[(-1)^m LegendreP[n, m, 2, z] LegendreP[n, -m, 2, z], {m, -n, n}] == 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "n"]]]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", RowBox[List["LegendreP", "[", RowBox[List["n", ",", "m", ",", "2", ",", "z"]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List["n", ",", RowBox[List["-", "m"]], ",", "2", ",", "z"]], "]"]]]]]], "\[Equal]", "1"]]]]

 MathML Form

 m = - n n ( - 1 ) m P TagBox["P", LegendreP] n m ( z TagBox["z", HoldComplete[LegendreP, 2]] ) P TagBox["P", LegendreP] n - m ( z TagBox["z", HoldComplete[LegendreP, 2]] ) 1 m -1 n n -1 m LegendreP n m 2 z LegendreP n -1 m 2 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m_", "=", RowBox[List["-", "n_"]]]], "n_"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m_"], " ", RowBox[List["LegendreP", "[", RowBox[List["n_", ",", "m_", ",", "2", ",", "z_"]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List["n_", ",", RowBox[List["-", "m_"]], ",", "2", ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "1"]]]]

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

 2001-10-29