#11164: Integral of sin(x)/x gives false result.
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Reporter: benreynwar | Owner: burcin
Type: defect | Status:
Priority: major | needs_info
Component: calculus | Milestone:
Keywords: | Resolution:
Authors: | Merged in:
Report Upstream: Reported upstream. No | Reviewers:
feedback yet. | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by kcrisman):
> > > What if we don't allow incomplete gamma to become `Ei` when the
first arg is zero - would that solve the branch problem?
> > Looks like if that was once possible, it isn't any more (already done
during integration in Maxima, I mean).
> Or maybe not;
Drivel. We could try this, though the branch problem is likely still
there with incomplete gamma.
{{{
sage: maxima_calculus('integrate(sin(x)/x,x)')
-(%i*gamma_incomplete(0,%i*x)-%i*gamma_incomplete(0,-%i*x))/2
sage: maxima_calculus('integrate(sin(x)/x,x)').sage()
-1/2*I*Ei(I*x) + 1/2*I*Ei(-I*x)
}}}
because we do
{{{
if x == 0:
return -Ei(-y)
}}}
in sage/functions/other.py
But unfortunately
{{{
sage: i*CC(0).gamma_inc(-i/100000)-i*CC(0).gamma_inc(i/100000)
-3.14157265358979
}}}
So same problem there. Yuck. We really need Maxima to provide a proper
`Si` function, or somehow magically translate such combos ourselves with
pattern-matching, which sounds horrible too.
--
Ticket URL: <http://trac.sagemath.org/ticket/11164#comment:17>
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