Hand-to-hand combat with thousand-digit integrals

Title: Hand-to-hand combat with thousand-digit integrals
Creator: Bailey, David H.; Borwein, Jonathan M.
Relation: Journal of Computational Science Vol. 3, Issue 3, p. 77-86
Publisher Link: http://dx.doi.org/10.1016/j.jocs.2010.12.004
Publisher: Elsevier
Resource Type: journal article
Date: 2012
Description: In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multi-step uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K, K' , E and E' .We find that in many cases such integrals can be “experimentally” evaluated in closed form or that intriguing linear relations exist within a class of similar integrals. Discovering these identities and relations often requires the evaluation of integrals to extreme precision, combined with large-scale runs of the “PSLQ” integer relation algorithm. This paper presents details of the techniques used in these calculations and mentions some of the many difficulties that can arise.
Subject: experimental mathematics; high-precision computing; numerical integration; random walks; elliptic integrals
Identifier: http://hdl.handle.net/1959.13/940078
Identifier: uon:12944
Identifier: ISSN:1877-7503
Language: eng
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