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#2413 Shi (sinh integral) wrong branch, integrate inconsisten

closed
nobody
5
2012-05-27
2012-05-26
Anonymous
No

Note that expintegral_shi(x) is a real function - see A&S or Wolfram Alpha.

http://www.wolframalpha.com/input/?i=integrate+Shi%28x%29+from+0+to+1%2F2

gives about .125872409 as does mpmath.

(%i11) expand(float(integrate(expintegral_shi(x),x,0,1/2)));

(%o11) 1.5707963267948966*%i+.12587240970345281

Extra pi/2?

This come from

(%i30) float(expintegral_shi(1/2));

(%o30) 3.141592653589793*%i+0.506996749819667

So Maxima is, oddly, using a different branch for this function even though they cite

The Exponential Integral Shi(z) (A&S 5.2.3)

and http://people.math.sfu.ca/~cbm/aands/page_231.htm clearly makes this something that should be real.

See http://trac.sagemath.org/sage_trac/ticket/11143 where this was first noticed.

Discussion

  • Raymond Toy
    Raymond Toy
    2012-05-27

    Fixed in git.

    Thanks for the report.

     
  • Raymond Toy
    Raymond Toy
    2012-05-27

    • labels: 460522 --> Lisp Core - Floating point
    • status: open --> closed