Re: Problem with an integral
- To: mathgroup at smc.vnet.net
- Subject: [mg95617] Re: Problem with an integral
- From: dh <dh at metrohm.com>
- Date: Thu, 22 Jan 2009 07:14:39 -0500 (EST)
- References: <gl72ql$cpm$1@smc.vnet.net>
Hi, Integrate gives a generic result, that is correct for almost all values, but does NOT take into account special behaviour for isolated values. E.g. set k=1 and look at the result from Assuming[{ n > 0}, Integrate[fun, {x, 0, \[Infinity]}]]. The result has the form of a difference of 2 summands that both have no numerical value for n==1. Therefore, this formula can not be used for n==1. Due to numerical errors, it even fails for values of n close to 1. However, you may set k==1 and n==1, now Integrate gives the correct result. hope this helps, Daniel Jepessen wrote: > Hi. > > I'm working with a little problem in Mathematica 7.0.0. > I want to integrate this function > > fun = x^(n + 1)*E^(-x + (I*k)/x) > > Assuming that both n and k are greater than zero, I write > > integral = FullSimplify[Assuming[{k > 0, n > 0}, Integrate[fun, {x, 0, > \[Infinity]}]]] > > And I obtain a symbolic result. > But, when I want to put some specific value, like this > > integral /. {n -> 1, k -> 1} > > I obtain always ComplexInfinity, and/or other errors. > So, I've tried to evaluate numerically the integral for the same > specific values, in this way > > NIntegrate[Evaluate[fun /. {n -> 1, k -> 1}], {x, 0, \[Infinity]}] > > And I obtain a finite numeric result. So, there's some error in > symbolic computation, or I miss something when I try to integrate the > formula? > > Thanks for answers >