Re: Bessel K expansion, large argument?

*To*: mathgroup at smc.vnet.net*Subject*: [mg70120] Re: Bessel K expansion, large argument?*From*: Joel Storch <jstorch at earthlink.net>*Date*: Wed, 4 Oct 2006 05:59:35 -0400 (EDT)*References*: <eftdhr$6b9$1@smc.vnet.net>

The fuction in question has an esential singularity at the origin. To obtain the desired expansion, use the Mathematica command Series[z BesselK[1,z]/BesselK[0,z],{z,Infinity,2}] and you will obtain: z+1/2-1/(8z)+1/(8z^2) 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. >