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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
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