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.
>