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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions





http://functions.wolfram.com/07.14.26.0010.01









  


  










Input Form





(1 + z)^(\[Lambda] - 1/2) GegenbauerC[\[Nu], \[Lambda], 2/z + 1] == ((Cos[(\[Lambda] + \[Nu]) Pi] Pochhammer[2 \[Lambda], \[Nu]])/ (Cos[\[Lambda] Pi] Gamma[1/2 - \[Lambda]] Gamma[\[Nu] + 1])) MeijerG[{{\[Lambda] + 1/2}, {2 \[Lambda]}}, {{-\[Nu], 2 \[Lambda] + \[Nu]}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z_"]], ")"]], RowBox[List["\[Lambda]_", "-", FractionBox["1", "2"]]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", RowBox[List[FractionBox["2", "z_"], "+", "1"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["\[Lambda]", "+", "\[Nu]"]], ")"]], " ", "\[Pi]"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["2", " ", "\[Lambda]"]], ",", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["\[Lambda]", "+", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["2", " ", "\[Lambda]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List[RowBox[List["2", " ", "\[Lambda]"]], "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Lambda]", " ", "\[Pi]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "\[Lambda]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29