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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Expansions in 1/(1-z)





http://functions.wolfram.com/07.05.06.0079.01









  


  










Input Form





ChebyshevU[\[Nu], z] == ((2^(-2 - \[Nu]) Sqrt[1 - z] (-1 + z)^\[Nu])/ Sqrt[-1 - z]) (1 + Sqrt[(1 + z)/(-1 + z)])^(2 \[Nu] + 2) - ((2^\[Nu] Sqrt[1 - z] (-1 + z)^(-2 - \[Nu]))/Sqrt[-1 - z]) (1 + Sqrt[(z + 1)/(z - 1)])^(-2 \[Nu] - 2) /; !IntervalMemberQ[Interval[{-1, 1}], z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "\[Nu]"]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[FractionBox[RowBox[List["1", "+", "z"]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]]], ")"]], RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "2"]]]]], "-", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]]]]], ")"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]], "-", "2"]]]]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "\[Nu]"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[FractionBox[RowBox[List["1", "+", "z"]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]]], ")"]], RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "2"]]]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]]]]], ")"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]], "-", "2"]]]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2007-05-02





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