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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 ;)


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