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BesselK






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.04.06.0045.01









  


  










Input Form





BesselK[\[Nu], z] \[Proportional] ((1/2) Sqrt[Pi/2] Csc[Pi \[Nu]] (E^(I Sqrt[-z^2] + (I Pi (3 - 2 \[Nu]))/4) ((-E^(I Pi \[Nu])) (-z)^\[Nu] + z^\[Nu]) (1 + (I (-1 + 4 \[Nu]^2))/(8 Sqrt[-z^2]) + (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2) + \[Ellipsis]) + E^((-I) Sqrt[-z^2] + (I Pi (1 - 2 \[Nu]))/4) ((-z)^\[Nu] - E^(I Pi \[Nu]) z^\[Nu]) (1 - (I (-1 + 4 \[Nu]^2))/(8 Sqrt[-z^2]) + (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2) + \[Ellipsis])))/ (-z^2)^((1/4) (1 + 2 \[Nu])) /; (Abs[z] -> Infinity)










Standard Form





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MathML Form







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</ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <imaginaryi /> <pi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; 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Rule Form





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





2007-05-02





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