On recurrences for Ising integrals
نویسندگان
چکیده
منابع مشابه
On Recurrences for Ising Integrals
We use WZ-summation methods to compute recurrences for the Ising-class integrals Cn,k. In this context, we describe an algorithmic approach to obtain homogeneous and inhomogeneous recurrences for a general class of multiple contour integrals of Barnes’ type.
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From an experimental-mathematical perspective we analyze " Ising-class " integrals. These are structurally related n-dimensional integrals we call C n , D n , E n , where D n is a magnetic susceptibility integral central to the Ising theory of solid-state physics. We first analyze C n := 4 n! ∞ 0 · · · ∞ 0 1 n j=1 (u j + 1/u j) 2 du 1 u 1 · · · du n u n. We had conjectured—on the basis of extre...
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In recent work on multivariate elliptic hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group E7. In the present note, we consider the action of the affine Weyl group, or more precisely, the recurrences satisfied by special cases of the integral. These are of t...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2010
ISSN: 0196-8858
DOI: 10.1016/j.aam.2008.05.004