Opened 8 years ago

Last modified 3 years ago

#12145 new defect

Ugly result for exponential integral

Reported by: mjo Owned by: burcin
Priority: minor Milestone: sage-6.4
Component: calculus Keywords:
Cc: kcrisman Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

As reported in this sage-support thread:

​http://groups.google.com/group/sage-support/browse_thread/thread/793c2bdb3db1f02c

We expect, 

sage: integral( x / (exp(x) - 1) , (x,0,oo))
pi^2/6

but get, 

sage: integral( x / (exp(x) - 1) , (x,0,oo))
-1/6*pi^2 + limit(-1/2*x^2 + x*log(-e^x + 1) + polylog(2, e^x), x, +Infinity)

The above might not be incorrect, but it is not very useful either.

Change History (7)

comment:1 Changed 8 years ago by kcrisman

  • Cc kcrisman added
  • Component changed from symbolics to calculus
  • Priority changed from major to minor

comment:2 Changed 8 years ago by mjo

Same result from Maxima 5.27: 

(%i1) display2d: false;

(%o1) false
(%i2) f: x/(%e^x - 1);

(%o2) x/(%e^x-1)
(%i3) integrate(f, x, 0, inf);

(%o3) 'limit(li[2](%e^x)+x*log(1-%e^x)-x^2/2,x,inf,minus)-%pi^2/6

comment:3 Changed 6 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:4 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:5 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:6 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:7 Changed 3 years ago by mforets

more tests: 

sage: giac('integrate(x / (exp(x) - 1), x, 0, inf)')
pi^2/6
sage: integrate(x / (exp(x) - 1), x, 0, oo, algorithm='sympy')
integrate(x/(e^x - 1), x, 0, +Infinity)

i think this is another reason to make more user friendly the functionality that is offered through giac; stay tuned at the ​giac interface wiki.

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