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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Representations through more general functions > Through hypergeometric functions > Involving 1F1





http://functions.wolfram.com/03.03.26.0091.01









  


  










Input Form





BesselY[\[Nu], z] == (-((2^\[Nu] Gamma[\[Nu]])/(z^\[Nu] E^(I z) Pi))) Hypergeometric1F1[1/2 - \[Nu], 1 - 2 \[Nu], 2 I z] - ((1/(2^\[Nu] Pi)) Cos[\[Nu] Pi] Gamma[-\[Nu]] z^\[Nu] Hypergeometric1F1[1/2 + \[Nu], 1 + 2 \[Nu], 2 I z])/E^(I z) /; !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Hypergeometric1F1 </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <notin /> <ci> &#957; </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]]]], ")"]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ",", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ",", RowBox[List["2", " ", "\[ImaginaryI]", " ", "z"]]]], "]"]]]], "\[Pi]"]]], "-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Cos", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["-", "\[Nu]"]], "]"]], " ", SuperscriptBox["z", "\[Nu]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], ",", RowBox[List["2", " ", "\[ImaginaryI]", " ", "z"]]]], "]"]]]], "\[Pi]"]]], "/;", RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]










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





2007-05-02





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