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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/z





http://functions.wolfram.com/07.05.06.0073.01









  


  








Input Form





ChebyshevU[\[Nu], z] == 2^\[Nu] z^\[Nu] Hypergeometric2F1[-(\[Nu]/2), (1 - \[Nu])/2, -\[Nu], 1/z^2] - 2^(-\[Nu] - 2) z^(-\[Nu] - 2) Hypergeometric2F1[(3 + \[Nu])/2, (2 + \[Nu])/2, 2 + \[Nu], 1/z^2] /; !IntervalMemberQ[Interval[{-1, 0}], z] && !Element[\[Nu], Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["2", "\[Nu]"], SuperscriptBox["z", "\[Nu]"], RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["-", "\[Nu]"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "2"]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "2"]]], RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["3", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"], ",", RowBox[List["2", "+", "\[Nu]"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "]"]]]]]]]]








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[RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["-", "\[Nu]"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "2"]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "2"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["3", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"], ",", RowBox[List["2", "+", "\[Nu]"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]], "&&", RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]]]


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





2007-05-02