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 GegenbauerC

 http://functions.wolfram.com/07.13.26.0001.01

 Input Form

 GegenbauerC[\[Nu], z] == (2/\[Nu]) HypergeometricPFQ[{-\[Nu], \[Nu]}, {1/2}, (1 - z)/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["2", "\[Nu]"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "\[Nu]"]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]]]]]]

 MathML Form

 C ν ( 0 ) ( z ) 2 ν 2 F 1 ( - ν , ν ; 1 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["-", "\[Nu]"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Nu]", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "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] GegenbauerC ν 0 z 2 ν -1 HypergeometricPFQ -1 ν ν 1 2 1 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "\[Nu]"]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]], "\[Nu]"]]]]]

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

 2001-10-29