* [ANNOUNCE] Efficient Algo for Polylog and Hurwitz Zeta
@ 2007-02-12 18:27 Linas Vepstas
0 siblings, 0 replies; only message in thread
From: Linas Vepstas @ 2007-02-12 18:27 UTC (permalink / raw)
To: gmp-discuss, gsl-discuss
Hi,
I've just posted a paper describing an efficient algorithm for
computing the (classical, fractional) polylogarithm Li_s(z)
for arbitrary complex values of s and z; and similarly for the
the Hurwitz zeta function.
http://arxiv.org/abs/math.CA/0702243
The algorithm generalizes Borwein's "An Efficient Algorithm for
the Riemann zeta function", and, draws on Cohen, Villegas and
Zagier "Convergence Acceleration for Alternating Series" to
propose a way of accelerating general oscillatory series.
The paper also provides a low-brow review of the monodromy of
the polylogarithm, as there does not appear to be any simple
discussion in the literature.
The algo is implemented in GMP, and the source code is available
upon request, under the LGPL license.
--linas
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2007-02-12 18:27 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2007-02-12 18:27 [ANNOUNCE] Efficient Algo for Polylog and Hurwitz Zeta Linas Vepstas
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for read-only IMAP folder(s) and NNTP newsgroup(s).