#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: Fixed upstream, in a later | Reviewers:
stable release. | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
The problem is caused by the integral being computed via symbolic
integration; see also comment:5. Maxima integrates `exp(x)/x` to
`-gamma_incomplete(0, -x)`, which is in principle correct, but only gives
a certain branch of the integral. The branch cut chosen for the
incomplete Gamma function is along the negative real axis. When using
this to compute `integrate(sin(x)/x, x, -1, 1)`, the two terms coming from
`exp(%i*x)` and `exp(-%i*x)` have branch cuts along the negative and
positive imaginary axis, respectively, so the sum has a branch cut along
the whole imaginary axis and therefore can't be the antiderivative of
`sin(x)/x`, which is an entire function.
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Ticket URL: <http://trac.sagemath.org/ticket/11164#comment:11>
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