- Title
- Advances in the theory of box integrals
- Creator
- Bailey, D. H.; Borwein, J. M.; Crandall, R. E.
- Relation
- Mathematics of Computation Vol. 79, Issue 271, p. 1839-1866
- Publisher Link
- http://dx.doi.org/10.1090/S0025-5718-10-02338-0
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2010
- 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.
- Subject
- box integrals; experimental mathematics; hyperclosure; global analytic strategy
- Identifier
- http://hdl.handle.net/1959.13/932067
- Identifier
- uon:11249
- Identifier
- ISSN:0025-5718
- Rights
- First published in Mathematics of Computation in Vol. 79, Issue 271, p. 1839-1866, 2010 published by the American Mathematical Society
- Language
- eng
- Full Text
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