Evaluation of AiryAi on the complex plane
- To: mathgroup at smc.vnet.net
- Subject: [mg44943] Evaluation of AiryAi on the complex plane
- From: mbedoya at tutopia.com (Mauricio Bedoya)
- Date: Wed, 10 Dec 2003 04:01:48 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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]]