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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Representations through more general functions > Through Meijer G > Classical cases involving unit step theta





http://functions.wolfram.com/05.09.26.0015.01









  


  










Input Form





UnitStep[1 - Abs[z]] (1 - z)^(\[Lambda] - 1/2) GegenbauerC[n, \[Lambda], 2 z - 1] == (Pochhammer[2 \[Lambda], n]/Gamma[n + 1]) Gamma[\[Lambda] + 1/2] MeijerG[{{}, {1/2 + \[Lambda] + n, 1/2 - \[Lambda] - n}}, {{0, 1/2 - \[Lambda]}, {}}, 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[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z_"]], ")"]], RowBox[List["\[Lambda]_", "-", FractionBox["1", "2"]]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", RowBox[List[RowBox[List["2", " ", "z_"]], "-", "1"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["2", " ", "\[Lambda]"]], ",", "n"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Lambda]", "+", FractionBox["1", "2"]]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Lambda]", "+", "n"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Lambda]", "-", "n"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List[FractionBox["1", "2"], "-", "\[Lambda]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["n", "+", "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





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