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>