Advances in the theory of box integrals

摘要: Box integrals - expectations or over the unit n-cube (or n-box) have 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 n {le} 4 dimensions box are any integer s hypergeometrically in sense clarify herein. For = 5 dimensions, show single unresolved integral call K{sub 5} stands way of such hyperclosure proofs. We supply compendium exemplary naturally arise algorithmically from this theory.