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 BesselY

 http://functions.wolfram.com/03.03.06.0021.01

 Input Form

 BesselY[\[Nu], z] \[Proportional] 4 I BesselJ[\[Nu], Subscript[z, 0]] Cos[Pi \[Nu]]^2 Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] + BesselY[\[Nu], Subscript[z, 0]]/ ((1/Subscript[z, 0])^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)])) + (1/2) (4 I (BesselJ[-1 + \[Nu], Subscript[z, 0]] - BesselJ[1 + \[Nu], Subscript[z, 0]]) Cos[Pi \[Nu]]^2 Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] + (BesselY[-1 + \[Nu], Subscript[z, 0]] - BesselY[1 + \[Nu], Subscript[z, 0]])/((1/Subscript[z, 0])^ (\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]))) (z - Subscript[z, 0]) + (1/8) (4 I (BesselJ[-2 + \[Nu], Subscript[z, 0]] - 2 BesselJ[\[Nu], Subscript[z, 0]] + BesselJ[2 + \[Nu], Subscript[z, 0]]) Cos[Pi \[Nu]]^2 Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)] + (BesselY[-2 + \[Nu], Subscript[z, 0]] - 2 BesselY[\[Nu], Subscript[z, 0]] + BesselY[2 + \[Nu], Subscript[z, 0]])/((1/Subscript[z, 0])^ (\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(\[Nu] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]))) (z - Subscript[z, 0])^2 + O[(z - Subscript[z, 0])^3]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", SubscriptBox["z", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", SubscriptBox["z", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["1", SubscriptBox["z", "0"]], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SubsuperscriptBox["z", "0", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]], "-", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["BesselY", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]], "-", RowBox[List["BesselY", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["1", SubscriptBox["z", "0"]], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SubsuperscriptBox["z", "0", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]], "-", RowBox[List["2", " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", SubscriptBox["z", "0"]]], "]"]]]], "+", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["BesselY", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]], "-", RowBox[List["2", " ", RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", SubscriptBox["z", "0"]]], "]"]]]], "+", RowBox[List["BesselY", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", SubscriptBox["z", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["1", SubscriptBox["z", "0"]], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SubsuperscriptBox["z", "0", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], " ", "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "3"], "]"]]]]]]]]

 MathML Form

 Y ν ( z ) Y ν ( z 0 ) ( 1 z 0 ) - ν arg ( z - z 0 ) 2 π z 0 - ν arg ( z - z 0 ) 2 π + 4 J ν ( z 0 ) cos 2 ( π ν ) arg ( z - z 0 ) 2 π arg ( z 0 ) + π 2 π + 1 2 ( ( Y ν - 1 ( z 0 ) - Y ν + 1 ( z 0 ) ) ( 1 z 0 ) - ν arg ( z - z 0 ) 2 π z 0 - ν arg ( z - z 0 ) 2 π + 4 ( J ν - 1 ( z 0 ) - J ν + 1 ( z 0 ) ) cos 2 ( π ν ) arg ( z - z 0 ) 2 π arg ( z 0 ) + π 2 π ) ( z - z 0 ) + 1 8 ( ( Y ν - 2 ( z 0 ) - 2 Y ν ( z 0 ) + Y ν + 2 ( z 0 ) ) ( 1 z 0 ) - ν arg ( z - z 0 ) 2 π z 0 - ν arg ( z - z 0 ) 2 π + 4 ( J ν - 2 ( z 0 ) - 2 J ν ( z 0 ) + J ν + 2 ( z 0 ) ) cos 2 ( π ν ) arg ( z - z 0 ) 2 π arg ( z 0 ) + π 2 π ) ( z - z 0 ) 2 + O ( ( z - z 0 ) 3 ) Proportional BesselY ν z BesselY ν Subscript z 0 1 Subscript z 0 -1 -1 ν z -1 Subscript z 0 2 -1 Subscript z 0 -1 ν z -1 Subscript z 0 2 -1 4 BesselJ ν Subscript z 0 ν 2 z -1 Subscript z 0 2 -1 Subscript z 0 2 -1 1 2 BesselY ν -1 Subscript z 0 -1 BesselY ν 1 Subscript z 0 1 Subscript z 0 -1 -1 ν z -1 Subscript z 0 2 -1 Subscript z 0 -1 ν z -1 Subscript z 0 2 -1 4 BesselJ ν -1 Subscript z 0 -1 BesselJ ν 1 Subscript z 0 ν 2 z -1 Subscript z 0 2 -1 Subscript z 0 2 -1 z -1 Subscript z 0 1 8 BesselY ν -2 Subscript z 0 -1 2 BesselY ν Subscript z 0 BesselY ν 2 Subscript z 0 1 Subscript z 0 -1 -1 ν z -1 Subscript z 0 2 -1 Subscript z 0 -1 ν z -1 Subscript z 0 2 -1 4 BesselJ ν -2 Subscript z 0 -1 2 BesselJ ν Subscript z 0 BesselJ ν 2 Subscript z 0 ν 2 z -1 Subscript z 0 2 -1 Subscript z 0 2 -1 z -1 Subscript z 0 2 O z -1 Subscript z 0 3 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["zz", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", SubscriptBox["zz", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["1", SubscriptBox["zz", "0"]], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SubsuperscriptBox["zz", "0", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", SubscriptBox["zz", "0"]]], "]"]], "-", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", SubscriptBox["zz", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["zz", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["BesselY", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", SubscriptBox["zz", "0"]]], "]"]], "-", RowBox[List["BesselY", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", SubscriptBox["zz", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["1", SubscriptBox["zz", "0"]], ")"]], RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SubsuperscriptBox["zz", "0", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ",", SubscriptBox["zz", "0"]]], "]"]], "-", RowBox[List["2", " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", SubscriptBox["zz", "0"]]], "]"]]]], "+", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", SubscriptBox["zz", "0"]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02