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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/07.05.06.0028.01









  


  










Input Form





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










Standard Form





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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[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "k"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", RowBox[List["1", "-", "z"]]], ")"]], "k"]]], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["2", " ", "\[Nu]"]]]], ",", "k"]], "]"]]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", 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["\[Nu]", "+", FractionBox["1", "2"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], "\[GreaterEqual]", "0"]]]]]]]]]]










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





2001-10-29





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