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 ChebyshevU

 http://functions.wolfram.com/05.05.06.0020.01

 Input Form

 ChebyshevU[n, z] == Sum[2^k GegenbauerC[n - k, k + 1, Subscript[z, 0]] (z - Subscript[z, 0])^k, {k, 0, n}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", "k"], RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", RowBox[List["k", "+", "1"]], ",", SubscriptBox["z", "0"]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "k"]]]]]]]]]

 MathML Form

 U n ( z ) k = 0 n 2 k C n - k k + 1 ( z 0 ) ( z - z 0 ) k ChebyshevU n z k 0 n 2 k Subscript C n -1 k k 1 Subscript z 0 z -1 Subscript z 0 k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevU", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", "k"], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", RowBox[List["k", "+", "1"]], ",", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]]]]]]]]

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

 2007-05-02