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Re: Bessel K expansion, large argument?

• To: mathgroup at smc.vnet.net
• Subject: [mg70113] Re: [mg70088] Bessel K expansion, large argument?
• From: Gerry Flanagan <flanagan at materials-sciences.com>
• Date: Wed, 4 Oct 2006 05:59:04 -0400 (EDT)
• References: <200610031016.GAA06359@smc.vnet.net>

If you ignore the error messages,
Simplify[Series[z*(BesselK[1, z]/BesselK[0, z]),  {z, Infinity, 2}]]
gives the result you're looking for.
Gerry F.


AES wrote:

>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.
>
>
>  
>

• References:
  • Bessel K expansion, large argument?
    • From: AES <siegman@stanford.edu>