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.
@article{832,
title = {Euler's divergent series and an elementary model in Statistical Physics},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {12},
year = {2016},
doi = {10.26493/1855-3974.832.987},
language = {EN},
url = {http://dml.mathdoc.fr/item/832}
}
Allombert, Bill; Allouche, Jean-Paul Simon; Mendès France, Michel. Euler's divergent series and an elementary model in Statistical Physics. ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016) . doi : 10.26493/1855-3974.832.987. http://gdmltest.u-ga.fr/item/832/