Re: Bessel K expansion, large argument?

*To*: mathgroup at smc.vnet.net*Subject*: [mg70127] Re: Bessel K expansion, large argument?*From*: "sashap" <pavlyk at gmail.com>*Date*: Wed, 4 Oct 2006 06:00:11 -0400 (EDT)*References*: <eftdhr$6b9$1@smc.vnet.net>

In v 5.2: In[1]:= Series[z*(BesselK[1, z]/BesselK[0, z]), {z, Infinity, 3}] <messages suppressed> Out[1]= SeriesData[z, Infinity, {1, 0, 1/2, 0, -1/8, 0, 1/8, 0, -25/128}, -2, 7, 2] thus the answer w + 1/2 - 1/8 1/w +1/64/w^2 + ... Oleksandr Pavlyk Special Functions Developer Wolfram Research 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.