- Title
- Box integrals
- Creator
- Bailey, D. H.; Borwein, J. M.; Crandall, R. E.
- Relation
- Journal of Computational and Applied Mathematics Vol. 206, Issue 1, p. 196-208
- Publisher Link
- http://dx.doi.org/10.1016/j.cam.2006.06.010
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2007
- Description
- By a “box integral” we mean here an expectation <|→/r − →/q|s> where →/r runs over the unit n-cube, with →/q and s fixed, explicitly: ∫₀¹...∫₀¹((r₁-q₁)²+...+(rn-qn)²)s/2dr₁...drn. The study of box integrals leads one naturally into several disparate fields of analysis. While previous studies have focused upon symbolic evaluation and asymptotic analysis of special cases (notably s = 1), we work herein more generally—in interdisciplinary fashion—developing results such as: (1) analytic continuation (in complex s), (2) relevant combinatorial identities, (3) rapidly converging series, (4) statistical inferences, (5) connections to mathematical physics, and (6) extreme-precision quadrature techniques appropriate for these integrals. These intuitions and results open up avenues of experimental mathematics, with a view to new conjectures and theorems on integrals of this type.
- Subject
- box integrals; multi-dimensional integrals; high-precision quadrature
- Identifier
- http://hdl.handle.net/1959.13/940735
- Identifier
- uon:13095
- Identifier
- ISSN:0377-0427
- Language
- eng
- Full Text
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