#16671: implement harmonic number function H(n,m)
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Reporter: rws | Owner:
Type: | Status: needs_work
defect | Milestone: sage-6.4
Priority: major | Resolution:
Component: | Merged in:
symbolics | Reviewers:
Keywords: | Work issues: merge fix for #17790
special, log | Commit:
Authors: Ralf | ca696281c6d2425b72d72b6408e4a787b32d637a
Stephan | Stopgaps:
Report Upstream: N/A |
Branch: |
u/rws/16671 |
Dependencies: |
#17790 |
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Comment (by rws):
Let's document here that both forms for the generalized harmonic numbers
{{{
H(q/p,m) = zeta(m) - p^m * sum(1/(q+p*k)^m, k, 1, oo) (Wikipedia
2015-Mar-07)
H(k,n) = binomial(n+k-1,k-1)*(harmonic_number(n+k-1)-harmonic_number(k-1))
(http://mathworld.wolfram.com/HarmonicNumber.html eq. 55)
}}}
are both wrong, with the counterexamples `H(5/2,3)=1/27*sqrt(3) +
1/8*sqrt(2) + 1` and `H(5,3)=256103/216000`.
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Ticket URL: <http://trac.sagemath.org/ticket/16671#comment:63>
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