#12521: evaluate log gamma for complex input
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Reporter: kcrisman | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: basic arithmetic | Keywords: lgamma log_gamma
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Currently, we use MPFR or Ginac to evaluate `log_gamma`, but this returns
`NaN` for negative input with even ceiling.
{{{
sage: log_gamma(-2.1)
NaN
sage: log_gamma(-3.1)
0.400311696703985
sage: log_gamma(-4.1)
NaN
sage: log_gamma(-5.1)
-2.63991581673655
sage: log_gamma(-21/10).n()
NaN
sage: get_systems('log_gamma(-21/10).n()')
['ginac']
sage: log_gamma(CC(-2.1))
1.53171380819509 + 3.14159265358979*I
}}}
We can use mpmath or something other trick to get this to work, now that
#10075 has a nice symbolic function available. See #10072 for where we
originally got better numerical evaluation.
{{{
sage: mpmath.loggamma(-2.1)
mpc(real='1.5317138081950856', imag='-9.4247779607693793')
}}}
Putting as defect because there is a log gamma for negative numbers,
though we should talk about branches...
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12521>
Sage <http://www.sagemath.org>
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