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Re: Evaluation of AiryAi on the complex plane

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44959] Re: Evaluation of AiryAi on the complex plane
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 11 Dec 2003 05:28:05 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <br6oss$2lg$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

you know what you are doing ??
The Airy function decay exponential with
Exp[- 2 z^(3/2)/3] for Re[z]>0

for 11.18 this gives a factor of Exp[-25]
and you will need hig precision arithmetic
to evaluate that.

Regards
  Jens

Mauricio Bedoya wrote:
> 
> Hello:
> 
> I'm in trouble evaluating the AiryAi function. I need to evaluate it
> around the point (11.18,0) or (11.18 + I 0.0). When I sweep the real
> axis there is no problem [1], it has a value of 2 10^-12 on all the
> range.
> 
> But when I choose a range on a complex line [2], the function throws a
> 0 value on all the range.
> 
> when I evaluate the function [3] I obtain 0 in the complex plane
> around 11.18 and 2.31151*10^-12 in 11.18, no matter how close I am
> from 11.18 + 0.0 I.
> 
> This doesn't happen around the points 10.03 + 0.0 I and 23.52 + 0.0 I.
> 
> I work in mathemathica 4.1.2.0.
> 
> I have tried to evaluate the Ai function in the version 3 and the
> result is 0 in the complex plane, but when I plot the function with
> complex values I obtain values different from 0 and also the absolute
> value of the function is continuous. I think that there is a problem
> with the evaluation of the function around 11.18 because I plotted the
> function in mathematica 3 with no problems but I couldn't evaluate it.
> In the version 4 I couldn't plot or evaluate it.
> 
> I would be grateful if someone could help me with this problem.
> 
> Mauricio Bedoya
> 
> List of commands
> [1] Plot[{AiryAi[11.18 + x]}, {x, 0, 10^-100}, PlotRange -> {All, {0,
> 10^-11}}]
> [2] Plot[{AiryAi[11.18 + x I]}, {x, 0, 10^-100}, PlotRange -> {All,
> {0, 10^-11}}]
> [3] Abs[ai[11.18]]
>     Abs[ai[11.18 + 0 10^-11 I]]


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