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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/05.09.06.0030.01









  


  










Input Form





GegenbauerC[n, \[Lambda], z] == ((2^n Sqrt[Pi] Gamma[\[Lambda] + n/2])/(Gamma[\[Lambda]] Gamma[(1 - n)/2] n!)) Hypergeometric2F1[-(n/2), \[Lambda] + n/2, 1/2, z^2] + ((2^n Sqrt[Pi] z Gamma[\[Lambda] + (1 + n)/2])/ (Gamma[\[Lambda]] Gamma[1 - n/2] (n - 1)!)) Hypergeometric2F1[(1 - n)/2, \[Lambda] + (n + 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["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["\[Lambda]", "+", FractionBox["n", "2"]]], "]"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", RowBox[List["\[Lambda]", "+", FractionBox["n", "2"]]], ",", FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "\[Lambda]", "]"]], " ", RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "-", "n"]], "2"], "]"]], " ", RowBox[List["n", "!"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", "z", " ", RowBox[List["Gamma", "[", RowBox[List["\[Lambda]", "+", FractionBox[RowBox[List["1", "+", "n"]], "2"]]], "]"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "n"]], "2"], ",", RowBox[List["\[Lambda]", "+", FractionBox[RowBox[List["n", "+", "1"]], "2"]]], ",", FractionBox["3", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", "\[Lambda]", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["n", "2"]]], "]"]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]], "!"]]]]]]]]]]]










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





2007-05-02





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