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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/932067

Title: Advances in the theory of box integrals
Author/Creator: Bailey, D. H.; Borwein, J. M.; Crandall, R. E.
Institution: The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
Description: Box integrals - expectations 〈|r→|s or 〈|r→ - q→|s〉 over the unit n-cube - have over three decades been occasionally given closed forms for isolated n, s. By employing experimental mathematics together with a new, global analytic strategy, we prove that for each of n = 1, 2, 3, 4 dimensions the box integrals are for any integer s hypergeometrically closed ("hyperclosed") in an explicit sense we clarify herein. For n = 5 dimensions, such a complete hyperclosure proof is blocked by a single, unresolved integral we call K₅; although we do prove that all but a finite set of (n = 5) cases enjoy hyperclosure. We supply a compendium of exemplary closed forms that arise naturally from the theory.
Relation: Mathematics of Computation Vol. 79, Issue 271, p. 1839-1866
Publisher Link: http://dx.doi.org/10.1090/S0025-5718-10-02338-0
Date: 2010
Publisher: American Mathematical Society
Keyword(s): box integrals; experimental mathematics; hyperclosure; global analytic strategy
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/932067
Identifier: ISSN:0025-5718

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