Re: Evaluation of AiryAi on the complex plane
- To: mathgroup at smc.vnet.net
- Subject: [mg45008] Re: Evaluation of AiryAi on the complex plane
- From: "Kevin J. McCann" <kjm at KevinMcCann.com>
- Date: Fri, 12 Dec 2003 04:42:44 -0500 (EST)
- References: <br6oss$2lg$1@smc.vnet.net> <br9h81$cub$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I don't think that's the problem: Ai[200.0] returns 9.1536243084*10^-821 Kevin "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote in message news:br9h81$cub$1 at smc.vnet.net... > 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]] >