Re: Bessel K expansion, large argument?
- To: mathgroup at smc.vnet.net
- Subject: [mg70125] Re: [mg70088] Bessel K expansion, large argument?
- From: Carl Woll <carlw at wolfram.com>
- Date: Wed, 4 Oct 2006 05:59:51 -0400 (EDT)
- References: <200610031016.GAA06359@smc.vnet.net>
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.
>
>
In version 5.2 both:
Series[z BesselK[1, z]/BesselK[0, z], {z, Infinity, 2}]
and
z BesselK[1, z]/BesselK[0, z] + O[z, Infinity]^3
produce
1/(1/z) + 1/2 - 1/(8*z) + (1/8)*(1/z)^2 + O[z,Infinity]^3
Carl Woll
Wolfram Research
- References:
- Bessel K expansion, large argument?
- From: AES <siegman@stanford.edu>
- Bessel K expansion, large argument?