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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Integral representations > Contour integral representations





http://functions.wolfram.com/03.03.07.0006.01









  


  










Input Form





BesselY[\[Nu], z] == ((z^2)^(\[Nu]/2) (1/(2 Pi I)) ContourIntegral[(Gamma[\[Nu]/2 + s] Gamma[-(\[Nu]/2) + s])/ (Gamma[-((\[Nu] + 1)/2) + s] Gamma[(\[Nu] + 3)/2 - s])/(z^2/4)^s, \[ScriptCapitalL]["s"]])/z^\[Nu] - (((z^2)^\[Nu] - z^(2 \[Nu])) Cot[Pi \[Nu]] (1/(2 Pi I)) ContourIntegral[Gamma[s + \[Nu]/2]/Gamma[1 + \[Nu]/2 - s]/(z^2/4)^s, \[ScriptCapitalL]["s"]])/(z^\[Nu] (z^2)^(\[Nu]/2)) /; !Element[\[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["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["\[Nu]", "/", "2"]]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Nu]", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], "+", "s"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "2"], "4"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]]]], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["\[Nu]", "+", "3"]], "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]], "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["-", FractionBox["\[Nu]", "2"]]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], "\[Nu]"], "-", SuperscriptBox["z", RowBox[List["2", " ", "\[Nu]"]]]]], ")"]], " ", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox["\[Nu]", "2"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "2"], "4"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], "/;", RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]










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





2001-10-29





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