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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/05.09.06.0028.01









  


  










Input Form





GegenbauerC[n, \[Lambda], z] \[Proportional] (2^n Sqrt[Pi] Gamma[n/2 + \[Lambda]])/(Gamma[(1 - n)/2] n! Gamma[\[Lambda]]) + (2^n Sqrt[Pi] Gamma[(1 + n)/2 + \[Lambda]] z)/ (Gamma[1 - n/2] (n - 1)! Gamma[\[Lambda]]) - ((2 Cos[(n Pi)/2] Gamma[1 + n/2 + \[Lambda]])/(Gamma[\[Lambda]] Gamma[n/2])) z^2 - (2^n Sqrt[Pi] Gamma[(3 + n)/2 + \[Lambda]] z^3)/ (3 Gamma[1 - n/2] (n - 2)! Gamma[\[Lambda]]) + O[z^4]










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[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["n", "2"], "+", "\[Lambda]"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "-", "n"]], "2"], "]"]], " ", RowBox[List["n", "!"]], " ", RowBox[List["Gamma", "[", "\[Lambda]", "]"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "n"]], "2"], "+", "\[Lambda]"]], "]"]], " ", "z"]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["n", "2"]]], "]"]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]], "!"]], " ", RowBox[List["Gamma", "[", "\[Lambda]", "]"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "2"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", FractionBox["n", "2"], "+", "\[Lambda]"]], "]"]]]], ")"]], " ", SuperscriptBox["z", "2"]]], RowBox[List[RowBox[List["Gamma", "[", "\[Lambda]", "]"]], " ", RowBox[List["Gamma", "[", FractionBox["n", "2"], "]"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["3", "+", "n"]], "2"], "+", "\[Lambda]"]], "]"]], " ", SuperscriptBox["z", "3"]]], RowBox[List["3", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["n", "2"]]], "]"]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "2"]], ")"]], "!"]], " ", RowBox[List["Gamma", "[", "\[Lambda]", "]"]]]]], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "4"]]]]]]]










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





2007-05-02