منابع مشابه
Box Integrals
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:
متن کاملHigher-Dimensional Box Integrals
Herein, with the aid of substantial symbolic computation, we solve previously open problems in the theory of n-dimensional box integrals Bn(s) := 〈|~r|〉; ~r ∈ [0, 1]. In particular we resolve an elusive integral called K5 that previously acted as a blockade against closed-form evaluation in n = 5 dimensions. In consequence we now know that Bn(integer) can be given a closed form for n = 1, 2, 3,...
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Box integrals—expectations 〈|~r|〉 or 〈|~r − ~q|〉 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 clar...
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In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals. In the second step, these integrals are reformulated as improper integrals. We will show that these integrals can be...
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The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop calculations can be reduced to a small number of master integrals. An efficient method to compute these master integrals is to derive and solve differential equati...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.06.010