#15846: Incorrect series expansion of zeta(s) at 1
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Reporter: mmezzarobba | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by behackl):
* cc: behackl (added)
Comment:
I *think* I may have tracked down the reason for this back to !SymPy.
There, we have
{{{
>>> from sympy import zeta, gamma
>>> from sympy.abc import x
>>> gamma(x).series(x, x0=0, n=1)
1/x - EulerGamma + O(x)
}}}
that is, expanding the gamma function at a pole works. However, for the
zeta function:
{{{
>>> zeta(x).series(x, x0=1, n=1)
Traceback (most recent call last):
...
sympy.core.function.PoleError: Cannot expand zeta(_x + 1) around 0
}}}
This could be fixed by implementing `_eval_nseries` directly for `zeta`
(which can be found at `local/lib/python/site-
packages/sympy/functions/sepecial/zeta_functions.py`) intelligently enough
such that the pole at s=1 is handled. Unfortunately, I think there has to
be a discussion first how to handle the coefficients in this expansion
(cf. http://dlmf.nist.gov/25.2#E4). (AFAIK, the generalized Euler-
Mascheroni constants are currently **not** implemented symbolically...)
--
Ticket URL: <http://trac.sagemath.org/ticket/15846#comment:3>
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