科研之友
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摘要
Box integrals expectations <vertical bar(r) over right arrow vertical bar(s)> or <vertical bar(r) over right arrow-(q) over right arrow vertical bar(s)> over the unit ncube 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 kappa(5); 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.
- 出版日期2010-7
