2017/05/26 by Ovidiu Costin, Gerald V. Dunne, Gerald V Dunne
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Convergence (economics) #Convergent series #Divergence (linguistics) #Divergent series #Extrapolation #Factorial #Inverse #Mathematical functions and polynomials #Random Matrices and Applications #Resummation #Series (stratigraphy) #cond-mat.other #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aa9e30
published as J.Phys. A51 (2018) no.4, 04LT01 · 5 pages, 4 figures
arxiv created 2017/05/26 · openalex created_date 2017/06/05 · openalex publication_date 2017/11/29 · arxiv updated 2019/10/25 · openalex updated_date 2026/08/05
Abstract We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being convergent, these new series allow rigorous extrapolation from an asymptotic region with a large parameter, to the opposite region where the parameter is small. We illustrate the method with various physical examples, and discuss how these convergent series relate to standard methods such as Borel summation, and also how they incorporate the physical Stokes phenomenon. We comment on the relation of these results to Dyson’s physical argument for the divergence of perturbation theory. This approach also leads naturally to a wide class of relations between bosonic and fermionic partition functions, and Klein–Gordon and Dirac determinants.