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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Representations through more general functions > Through Meijer G > Classical cases involving unit step theta





http://functions.wolfram.com/07.05.26.0022.01









  


  










Input Form





Sqrt[-1 + z] (-1 + 2 z) UnitStep[-1 + Abs[z]] ChebyshevU[\[Nu], 1 - 8 z + 8 z^2] == (1/2) Sqrt[Pi] (1 + \[Nu]) MeijerG[{{-(3/2) - 2 \[Nu], 5/2 + 2 \[Nu]}, {}}, {{}, {-(1/2), 0}}, z] /; Re[z] > 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z_"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "z_"]]]], ")"]], " ", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]_", ",", RowBox[List["1", "-", RowBox[List["8", " ", "z_"]], "+", RowBox[List["8", " ", SuperscriptBox["z_", "2"]]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "-", RowBox[List["2", " ", "\[Nu]"]]]], ",", RowBox[List[FractionBox["5", "2"], "+", RowBox[List["2", " ", "\[Nu]"]]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "0"]], "}"]]]], "}"]], ",", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]










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





2001-10-29





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