#12521: evaluate log gamma for complex input
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Reporter: kcrisman | Owner: AlexGhitza
Type: defect | Status: new
Priority: critical | Milestone: sage-5.11
Component: basic arithmetic | Resolution:
Keywords: lgamma log_gamma | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Changes (by eviatarbach):
* priority: major => critical
Comment:
Our current implementation is wrong. For the principal branch,
`log_gamma(z)` should not be equal to `log(gamma(z))` in general. See
https://cs.uwaterloo.ca/research/tr/1994/23/CS-94-23.pdf:
`ln_gamma(x) = ln(gamma(x)) + 2*pi*i*ceil(x/2 - 1)`
Changing to critical because the documentation claims that it's the
principal branch, which is mathematically wrong.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12521#comment:8>
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