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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/07.04.26.0032.01









  


  










Input Form





ChebyshevT[\[Nu], z] == (((2^(-1 - \[Nu]) \[Nu])/Sqrt[Pi]) (4^\[Nu] MeijerG[{{1 - \[Nu], 1/2 - \[Nu]}, {}}, {{0}, {-2 \[Nu]}}, 2/(z - 1)] - (z - 1)^(2 \[Nu]) MeijerG[{{1 + \[Nu], 1/2 + \[Nu]}, {}}, {{0}, {2 \[Nu]}}, 2/(z - 1)]))/(z - 1)^\[Nu] /; !IntervalMemberQ[Interval[{-1, 1}], z] && !Element[2 \[Nu], Integers]










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[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", "\[Nu]"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["4", "\[Nu]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]], "}"]]]], "}"]], ",", FractionBox["2", RowBox[List["z", "-", "1"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List["2", " ", "\[Nu]"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["2", " ", "\[Nu]"]], "}"]]]], "}"]], ",", FractionBox["2", RowBox[List["z", "-", "1"]]]]], "]"]]]]]], ")"]]]], SqrtBox["\[Pi]"]], "/;", RowBox[List[RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]], "&&", RowBox[List["!", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "\[Element]", "Integers"]]]]]]]]]]]]










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





2007-05-02





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