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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/07.05.06.0024.01









  


  








Input Form





ChebyshevU[\[Nu], z] == 2^\[Nu] (z - 1)^\[Nu] Hypergeometric2F1[-\[Nu], -(1/2) - \[Nu], -1 - 2 \[Nu], 2/(1 - z)] - 2^(-\[Nu] - 2) (z - 1)^(-2 - \[Nu]) Hypergeometric2F1[2 + \[Nu], 3/2 + \[Nu], 3 + 2 \[Nu], 2/(1 - z)] /; !IntervalMemberQ[Interval[{-1, 1}], z] && !Element[2 \[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[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "\[Nu]"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["2", " ", "\[Nu]"]]]], ",", FractionBox["2", RowBox[List["1", "-", "z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ",", FractionBox["2", RowBox[List["1", "-", "z"]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List["2", "\[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[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "\[Nu]"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["2", " ", "\[Nu]"]]]], ",", FractionBox["2", RowBox[List["1", "-", "z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]], ",", RowBox[List["3", "+", RowBox[List["2", " ", "\[Nu]"]]]], ",", FractionBox["2", RowBox[List["1", "-", "z"]]]]], "]"]]]]]], "/;", 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)





2001-10-29