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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/05.04.26.0018.01









  


  








Input Form





(UnitStep[-1 + Abs[z]]/Sqrt[-1 + z^2]) ChebyshevT[n, 1/z] == Sqrt[Pi] Sqrt[z^2] MeijerG[{{-(1/2), 0}, {}}, {{}, {-((1 + n)/2), (1/2) (-1 + n)}}, z, 1/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z", "]"]]]], "]"]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]], RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", FractionBox["1", "z"]]], "]"]]]], "\[Equal]", RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[SuperscriptBox["z", "2"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "0"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["1", "+", "n"]], "2"]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", RowBox[List["ChebyshevT", "[", RowBox[List["n_", ",", FractionBox["1", "z_"]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z_", "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox["\[Pi]"], " ", SqrtBox[SuperscriptBox["z", "2"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "0"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]]]]


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





2001-10-29