#16671: implement harmonic number function H(n,m)
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.3
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> H_n belongs to the holonomic repertoir and should be available in Sage,
> both numerically and symbolically. For some info, see
> https://groups.google.com/forum/#!topic/sage-devel/uaA0yU7dZHU and
> https://en.wikipedia.org/wiki/Harmonic_number
New description:
H_n belongs to the holonomic repertoir and should be available in Sage,
both numerically and symbolically. For some info, see
https://groups.google.com/forum/#!topic/sage-devel/uaA0yU7dZHU and
https://en.wikipedia.org/wiki/Harmonic_number
This is actually a defect because we leave a Maxima result undefined:
{{{
sage: sum(1/k^3,k,1,n)
gen_harmonic_number(3, n)
sage: gen_harmonic_number?
Object `gen_harmonic_number` not found.
}}}
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Comment (by rws):
Replying to [comment:1 fredrik.johansson]:
> For exact values, FLINT has arith_harmonic_number()
Unfortunately, neither FLINT nor mpmath implements the generalized H(m,n)
returned by Maxima in the code example.
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Ticket URL: <http://trac.sagemath.org/ticket/16671#comment:2>
Sage <http://www.sagemath.org>
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