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Gradshteyn, I.S. and Rizhik, I.M. (1965) Table of Integrals Series and Products. Academic Press, Cambridge.

has been cited by the following article:

• TITLE: Brownian Motion in an External Field Revisited

  AUTHORS: Angelo Plastino, Mario Carlos Rocca, Diana Monteoliva, Alberto Hernando

  KEYWORDS: Divergent Partition Functions, Statistical Mechanics, Fisher Information

  JOURNAL NAME: Journal of Modern Physics, Vol.12 No.2, January 18, 2021

  ABSTRACT: In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.