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MathGroup Archive 2006

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Bessel K expansion, large argument?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70088] Bessel K expansion, large argument?
  • From: AES <siegman at stanford.edu>
  • Date: Tue, 3 Oct 2006 06:16:28 -0400 (EDT)
  • Organization: Stanford University

The function

      z BesselK[ 1, z ] / BesselK[ 0, z ]

with  z  complex, magnitude several times unity or larger, and argument 
between -90 and 90 degrees, appears in optical fiber mode calculations.

Experience shows that a quite good approximation to this is just

      w + 1/2

Can anyone suggest a next term or two in the expansion, e.g.

      w + 1/2 +  a/w + b/w^2    ???

Been trying to get Mathematica to tell me this, but not figuring out how 
to get the Series command to do what I want.


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