Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/932067
- Advances in the theory of box integrals
Bailey, D. H.;
Borwein, J. M.;
Crandall, R. E.
- The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
- 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.
- Mathematics of Computation Vol. 79, Issue 271, p. 1839-1866
- Publisher Link
- American Mathematical Society
global analytic strategy
- Resource Type
- journal article