barfing on an integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg6160] barfing on an integral*From*: peter <psalzman at landau.ucdavis.edu>*Date*: Thu, 27 Feb 1997 02:52:01 -0500*Sender*: owner-wri-mathgroup at wolfram.com

Hello All I'm trying to check my solution to approximations of integrals by the method of steepest decent. The integral i'm approximating is: I(x) = int e(x*t - e^t) dt from t=0 to t=infty my approximation is: J(x) = sqrt(2 Pi/x) * e^{1.5 x log x} The trouble is that MMA is barfing on I(x). If I try to do it analytically with Integrate[] it gives me a whole bunch of E^Infty terms. Most of which go to zero, but I'm having trouble getting MMA to actually evaluate the limit. N[%] doesn't seem to work, and MMA doesn't seem to realize that e^infty / e^e^infty is truly zero. Then I tried using NIntegrate on I(x), and it gave me a whole bunch of underflow errors, and said that the integrand is probably oscillatory (which it most certainly is not). I'm in a very awkward position. My approximation is only valid for large values of x (actually, I think anything over 10 will do). Yet, MMA barfs for large values of x. Is there some way I can check my approximation?? Much thanks. Peter -- Birthdays are good for you: A federal funded project has recently determined that people with the most number of birthdays will live the longest..... -=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=- I BOYCOTT ANY COMPANY THAT USES MASS ADVERTISING ON THE INTERNET