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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/07.14.26.0011.01









  


  








Input Form





(1 + z)^(-\[Nu] - 2 \[Lambda]) GegenbauerC[\[Nu], \[Lambda], (1 - z)/(1 + z)] == (1/(Gamma[2 \[Lambda]] Pochhammer[\[Lambda] + 1/2, \[Nu]] Gamma[\[Nu] + 1])) MeijerG[{{1 - 2 \[Lambda] - \[Nu], 1/2 - \[Nu] - \[Lambda]}, {}}, {{0}, {1/2 - \[Lambda]}}, z] /; !IntervalMemberQ[Interval[{-Infinity, -1}], 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[RowBox[List["-", "\[Nu]_"]], "-", RowBox[List["2", " ", "\[Lambda]_"]]]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", FractionBox[RowBox[List["1", "-", "z_"]], RowBox[List["1", "+", "z_"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", RowBox[List["2", " ", "\[Lambda]"]], "-", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]", "-", "\[Lambda]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], "-", "\[Lambda]"]], "}"]]]], "}"]], ",", "z"]], "]"]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", " ", "\[Lambda]"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["\[Lambda]", "+", FractionBox["1", "2"]]], ",", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29