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.