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 GegenbauerC

 http://functions.wolfram.com/07.14.26.0038.01

 Input Form

 UnitStep[Abs[z] - 1] (z^2 - 1)^(-\[Lambda] - n/2) GegenbauerC[n, \[Lambda], (2 z^2 - 1)/(2 z Sqrt[z^2 - 1])] == (((-1)^n Gamma[1 - \[Lambda]])/n!) MeijerG[{{1 - \[Lambda] - n/2, \[Lambda] - n/2}, {}}, {{}, {\[Lambda] + n/2, -(n/2)}}, z, 1/2] /; Element[n, Integers] && n >= 0 && Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "-", "1"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", FractionBox["n", "2"]]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n", ",", "\[Lambda]", ",", FractionBox[RowBox[List[RowBox[List["2", SuperscriptBox["z", "2"]]], "-", "1"]], RowBox[List["2", " ", "z", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Lambda]"]], "]"]]]], RowBox[List["n", "!"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Lambda]", "-", FractionBox["n", "2"]]], ",", RowBox[List["\[Lambda]", "-", FractionBox["n", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["\[Lambda]", "+", FractionBox["n", "2"]]], ",", RowBox[List["-", FractionBox["n", "2"]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

 MathML Form

 θ UnitStep ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" - 1 ) ( z 2 - 1 ) - n 2 - λ C n λ ( 2 z 2 - 1 2 z z 2 - 1 ) ( - 1 ) n Γ ( 1 - λ ) n ! G 2 , 2 0 , 2 ( z , 1 2 1 - n 2 - λ , λ - n 2 n 2 + λ , - n 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "2"]], RowBox[List["0", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["n", "2"], "-", "\[Lambda]"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["\[Lambda]", "-", FractionBox["n", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List[FractionBox["n", "2"], "+", "\[Lambda]"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["n", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] /; n Re ( z ) > 0 Condition UnitStep z -1 z 2 -1 -1 n 2 -1 -1 λ Subscript C n λ 2 z 2 -1 2 z z 2 -1 1 2 -1 -1 n Γ 1 -1 λ n -1 MeijerG 1 -1 n 2 -1 -1 λ λ -1 n 2 -1 n 2 -1 λ -1 n 2 -1 z 1 2 n z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["Abs", "[", "z_", "]"]], "-", "1"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]], ")"]], RowBox[List[RowBox[List["-", "\[Lambda]_"]], "-", FractionBox["n_", "2"]]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", FractionBox[RowBox[List[RowBox[List["2", " ", SuperscriptBox["z_", "2"]]], "-", "1"]], RowBox[List["2", " ", "z_", " ", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Lambda]"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Lambda]", "-", FractionBox["n", "2"]]], ",", RowBox[List["\[Lambda]", "-", FractionBox["n", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["\[Lambda]", "+", FractionBox["n", "2"]]], ",", RowBox[List["-", FractionBox["n", "2"]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["n", "!"]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]]]

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

 2001-10-29