Efficient Algo for Polylog and Hurwitz Zeta

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
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Dear Linas,

Thank you for your interest in our polylogs paper, and your
nice and 
efficient computations. In fact, I really wonder how
efficiently resurgent 
functions can be computed, but this is a slightly different
topic. I will 
have a closer look at your paper. A minor (stupid me!)
comment: my last 
name is misspelled in your [CG] reference.

With best regards,

Stavros

 
------------------------------------------------------------
-----------
| Stavros Garoufalidis            | Phone:     (404)
894-6614           |
| School of Mathematics           | FAX:       (404)
894-4409           |
| Georgia Institute of Technology | e-mail:    stavrosmath.gatech.edu  |
| Atlanta, GA  30332-0160, USA    | http://www.math.g
atech.edu/~stavros |
 
------------------------------------------------------------
-----------
On Mon, 12 Feb 2007, Linas Vepstas wrote:

>
> 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
>

-- 
 
------------------------------------------------------------
-----------
| Stavros Garoufalidis            | Phone:     (404)
894-6614           |
| School of Mathematics           | FAX:       (404)
894-4409           |
| Georgia Institute of Technology | e-mail:    stavrosmath.gatech.edu  |
| Atlanta, GA  30332-0160, USA    | http://www.math.g
atech.edu/~stavros |
 
------------------------------------------------------------
-----------
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