Re: complex output for real integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg115867] Re: complex output for real integral*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sun, 23 Jan 2011 05:36:37 -0500 (EST)

On 1/22/11 at 3:23 AM, tsariysk at craft-tech.com (Ted Sariyski) wrote: >I get complex answer for an integral from Exp[1/x^3]/x^3 over the >real axes: >In[]:=f[n_] = Assuming[ >{Element[x, Reals], Element[n, Integers], n >= 1}, >Integrate[E^(1/x^3)/x^3, {x, n, Infinity}] >] >Out[]:= 1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)]) >The imaginary part of f[n] is everywhere ~10^-16 and I could >ignore it but I guess there is a better approach. You could use Chop, i.e. In[7]:= ans = 1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)]); In[8]:= Chop[ans /. n -> 1 // N] Out[8]= 0.781197 But this is essentially the same as ignoring it. Note, the reason you are seeing this is due to the limitations of machine precision arithmetic. That is: In[9]:= Im[N[ans /. n -> 1, 50]] Out[9]= 0``50.25775441372254 Demonstrating the true value of the imaginary part is zero.