From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 14363 invoked by alias); 12 Feb 2007 18:27:29 -0000 Received: (qmail 14335 invoked by uid 22791); 12 Feb 2007 18:27:28 -0000 X-Spam-Check-By: sourceware.org Received: from e32.co.us.ibm.com (HELO e32.co.us.ibm.com) (32.97.110.150) by sourceware.org (qpsmtpd/0.31) with ESMTP; Mon, 12 Feb 2007 18:27:18 +0000 Received: from d03relay04.boulder.ibm.com (d03relay04.boulder.ibm.com [9.17.195.106]) by e32.co.us.ibm.com (8.12.11.20060308/8.13.8) with ESMTP id l1CIQkMF003374 for ; Mon, 12 Feb 2007 13:26:46 -0500 Received: from d03av02.boulder.ibm.com (d03av02.boulder.ibm.com [9.17.195.168]) by d03relay04.boulder.ibm.com (8.13.8/8.13.8/NCO v8.2) with ESMTP id l1CIRDOf521152 for ; Mon, 12 Feb 2007 11:27:14 -0700 Received: from d03av02.boulder.ibm.com (loopback [127.0.0.1]) by d03av02.boulder.ibm.com (8.12.11.20060308/8.13.3) with ESMTP id l1CIQlAO003032 for ; Mon, 12 Feb 2007 11:27:13 -0700 Received: from topology.austin.ibm.com (dyn95340159.austin.ibm.com [9.53.40.159]) by d03av02.boulder.ibm.com (8.12.11.20060308/8.12.11) with ESMTP id l1CIH1v6008018; Mon, 12 Feb 2007 11:17:01 -0700 Received: by topology.austin.ibm.com (Postfix, from userid 1000) id D4FF53A65A; Mon, 12 Feb 2007 12:16:47 -0600 (CST) Date: Mon, 12 Feb 2007 18:27:00 -0000 To: gmp-discuss@swox.com, gsl-discuss@sources.redhat.com Subject: [ANNOUNCE] Efficient Algo for Polylog and Hurwitz Zeta Message-ID: <20070212181647.GA923@austin.ibm.com> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.5.11 From: linas@austin.ibm.com (Linas Vepstas) Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org X-SW-Source: 2007-q1/txt/msg00012.txt.bz2 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