Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: Bessel K expansion, large argument?
  • Next by Date: Re: Smarter way to calculate middle-right terms of continued fraction partial sums
  • Previous by thread: Re: Bessel K expansion, large argument?
  • Next by thread: Draw approximated normal distribution based on mean, median, percentiles?