Re: Evaluation of AiryAi on the complex plane
- To: mathgroup at smc.vnet.net
- Subject: [mg44963] Re: Evaluation of AiryAi on the complex plane
- From: mbedoya at tutopia.com (Mauricio Bedoya)
- Date: Thu, 11 Dec 2003 05:28:08 -0500 (EST)
- References: <br6oss$2lg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hello:
I have found an alternative to eval the Ai function about 11.18+x I.
I expanded the function in a Taylor series around this point and it
gives a very good aproximation of the ayri function in the points
where Mathematica can evaluate it, so I guess that the aproximation in
the points where Mathematica cannot evaluate it is good.
Alt[z_] = Normal[Series[AiryAi[z], {z, 11.18, 30}]]
Mauricio
mbedoya at tutopia.com (Mauricio Bedoya) wrote in message news:<br6oss$2lg$1 at smc.vnet.net>...
> 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]]