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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/07.14.06.0050.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] == ((Cos[(Pi \[Nu])/2] Gamma[\[Nu]/2 + \[Lambda]])/(Gamma[\[Nu]/2 + 1] Gamma[\[Lambda]])) Hypergeometric2F1[-(\[Nu]/2), \[Lambda] + \[Nu]/2, 1/2, z^2] + ((2^\[Nu] Sqrt[Pi] Gamma[\[Lambda] + (1 + \[Nu])/2] z)/ (Gamma[\[Lambda]] Gamma[1 - \[Nu]/2] Gamma[\[Nu]])) Hypergeometric2F1[(1 - \[Nu])/2, \[Lambda] + (\[Nu] + 1)/2, 3/2, z^2]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Nu]", "2"], "+", "\[Lambda]"]], "]"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["\[Lambda]", "+", FractionBox["\[Nu]", "2"]]], ",", FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Nu]", "2"], "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", "\[Lambda]", "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["\[Lambda]", "+", FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"]]], "]"]], " ", "z"]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["\[Lambda]", "+", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"]]], ",", FractionBox["3", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "\[Lambda]", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]]]]]]]]]]]










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





2007-05-02





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