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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form > Using exponential function with branch cut-free arguments





http://functions.wolfram.com/03.03.06.0069.01









  


  










Input Form





BesselY[\[Nu], z] \[Proportional] (Csc[Pi \[Nu]]/(2 Sqrt[2 Pi])) ((Cos[\[Nu] Pi] (Exp[(-I) z - ((I Pi)/4) (1 + 2 \[Nu])] (-z)^(-(1/2) - \[Nu]) z^\[Nu] (1 - Sqrt[z^2]/z) + (Exp[(-I) z + ((I Pi)/4) (1 + 6 \[Nu])] ((-I) z)^\[Nu] (1 + Sqrt[z^2]/z))/(z^(1/2) (I z)^\[Nu])) - ((Exp[(-I) z - ((I Pi)/4) (1 - 2 \[Nu])] (-z)^(-(1/2) + \[Nu]) (1 - Sqrt[z^2]/z))/z^\[Nu] + (Exp[(-I) z + ((I Pi)/4) (1 - 6 \[Nu])] (I z)^\[Nu] (1 + Sqrt[z^2]/z))/(((-I) z)^\[Nu] z^(1/2)))) (1 + O[1/z]) + (Cos[\[Nu] Pi] (Exp[I z + ((I Pi)/4) (1 + 2 \[Nu])] (-z)^(-(1/2) - \[Nu]) z^\[Nu] (1 - Sqrt[z^2]/z) + (Exp[I z + ((I Pi)/4) (-1 + 2 \[Nu])] ((-I) z)^\[Nu] (1 + Sqrt[z^2]/z))/(z^(1/2) (I z)^\[Nu])) - ((Exp[I z + ((I Pi)/4) (1 - 2 \[Nu])] (-z)^(-(1/2) + \[Nu]) (1 - Sqrt[z^2]/z))/z^\[Nu] + (Exp[I z - ((I Pi)/4) (1 + 2 \[Nu])] (I z)^\[Nu] (1 + Sqrt[z^2]/z))/(((-I) z)^\[Nu] z^(1/2)))) (1 + O[1/z])) /; (Abs[z] -> Infinity) && !Element[\[Nu], Integers]










Standard Form





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MathML Form







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





2007-05-02





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