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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Representations through equivalent functions > With elementary functions





http://functions.wolfram.com/07.04.27.0013.01









  


  










Input Form





ChebyshevT[\[Nu], z] == ((1/2) (Cos[(Pi \[Nu])/2] (Sqrt[-z] + z^\[Nu] (-z)^(1/2 + \[Nu]) (1 + (Sqrt[z^2] Sqrt[-1 + z^2])/z^2)^(2 \[Nu])) + Sin[(Pi \[Nu])/2] (-Sqrt[z] + (-z)^\[Nu] z^(1/2 + \[Nu]) (1 + (Sqrt[z^2] Sqrt[-1 + z^2])/z^2)^(2 \[Nu]))))/ ((-z)^((\[Nu] + 1)/2) z^(\[Nu]/2) (1 + (Sqrt[z^2] Sqrt[-1 + z^2])/z^2)^ \[Nu]) /; !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["ChebyshevT", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["-", FractionBox["\[Nu]", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]], SuperscriptBox["z", "2"]]]], ")"]], RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["-", "z"]]], "+", RowBox[List[SuperscriptBox["z", "\[Nu]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]], SuperscriptBox["z", "2"]]]], ")"]], RowBox[List["2", " ", "\[Nu]"]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SqrtBox["z"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], "\[Nu]"], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]], SuperscriptBox["z", "2"]]]], ")"]], RowBox[List["2", " ", "\[Nu]"]]]]]]], ")"]]]]]], ")"]]]], "/;", 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)





2007-05-02





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