Re: complex output for real integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg115872] Re: complex output for real integral*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 23 Jan 2011 05:37:38 -0500 (EST)

f[n_Integer?Positive] = Assuming[ {Element[x, Reals], Element[n, Integers], n >= 1}, Integrate[E^(1/x^3)/x^3, {x, n, Infinity}]] 1/6 (-1)^(1/3) (-3 Gamma[5/3] + 2 Gamma[2/3, -(1/n^3)]) The imaginary part is less than 10^-100 for n <= 100 Union[Chop[Im /@ N[f /@ Range[100], 100], 10^-100]] {0} Bob Hanlon ---- Ted Sariyski <tsariysk at craft-tech.com> wrote: ============= Hi, 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. I'll appreciate any help. --Ted