Non-converging integral with linear transformation?!
- To: mathgroup at smc.vnet.net
- Subject: [mg101047] Non-converging integral with linear transformation?!
- From: mereandor <mereandor at gmail.com>
- Date: Mon, 22 Jun 2009 04:23:24 -0400 (EDT)
Hi!
I have a question regarding the Integral over the product of the two functions AiryAi and AiryAiPrime. Lets look at the following integrals:
f[x_] = AiryAi[-1 + 10^5 x] AiryAiPrime[-500 + 10^5 x]
NIntegrate[f[x], {x, 0, Infinity}]
10^-5*NIntegrate[f[x] /. x -> (10^-5 x), {x, 0, Infinity}]
Mathematica 6 seems to be unable to evaluate the first one; the result is 0 and a warning about to slow convergence is issued.
The second one is - as far as I know - the same as the first one but with a linear variable transformation applied -> this time the result is given without any warning.
So basically my question is: what is going on there? Am I doing something wrong?
thanks in advance for any hints ;)