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 GegenbauerC

 http://functions.wolfram.com/07.14.21.0001.01

 Input Form

 Integrate[GegenbauerC[\[Nu], \[Lambda], z], z] == GegenbauerC[\[Nu] + 1, \[Lambda] - 1, z]/(2 (\[Lambda] - 1))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "\[Lambda]", ",", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["\[Lambda]", "-", "1"]], ")"]]]]]]]]]

 MathML Form

 C ν λ ( z ) z 1 2 ( λ - 1 ) C ν + 1 λ - 1 ( z ) z Subscript C ν λ z 1 2 λ -1 -1 Subscript C ν 1 λ -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", "z_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["\[Lambda]", "-", "1"]], ")"]]]]]]]]]

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

 2001-10-29