Euler's divergent series and an elementary model in Statistical Physics

Bill Allombert, Jean-Paul Simon Allouche, Michel Mendès France


We discuss the multiple integral of a multivariate exponential taken with respect either to the Lebesgue measure or to the discrete uniform Bernoulli measure. In the first case the integral is linked to Euler's everywhere divergent power series and its generalizations, while in the second case the integral is linked to a one-dimensional model of spin systems as encountered in physics.


Euler divergent series, Abel-Plana Formula, Stirling numbers, spin system, Ising chain

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ISSN: 1855-3974

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