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 ChebyshevU

 http://functions.wolfram.com/05.05.26.0001.01

 Input Form

 ChebyshevU[n, z] == (n + 1) HypergeometricPFQ[{-n, n + 2}, {3/2}, (1 - z)/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List["n", "+", "2"]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]]]]]]

 MathML Form

 U n ( z ) ( n + 1 ) 2 F 1 ( - n , n + 2 ; 3 2 ; 1 - z 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"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["n", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List["1", "-", "z"]], "2"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ChebyshevU n z n 1 HypergeometricPFQ -1 n n 2 3 2 1 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevU", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List["n", "+", "2"]]]], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]]]]]]

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

 2001-10-29