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 ChebyshevT

 http://functions.wolfram.com/05.04.26.0002.01

 Input Form

 ChebyshevT[n, z] == (-1)^n HypergeometricPFQ[{-n, n}, {1/2}, (1 + z)/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", "n"]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox[RowBox[List["1", "+", "z"]], "2"]]], "]"]]]]]]]]

 MathML Form

 T n ( z ) ( - 1 ) n 2 F 1 ( - n , n ; 1 2 ; z + 1 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", "n"]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox["n", Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "2"], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List["z", "+", "1"]], "2"], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ChebyshevT n z -1 n Hypergeometric2F1 -1 n n 1 2 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevT", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", "n"]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox[RowBox[List["1", "+", "z"]], "2"]]], "]"]]]]]]]]

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

 2001-10-29