2010/01/05 by Jean Zinn‐Justin, Zinn-Justin, Jean · 1 citation
Mathematics · #Advanced Mathematical Identities #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1001.0675
openalex publication_date 2010/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade approximants, Borel--Pade summation, Borel transformation with mapping, which we briefly describe and one on which we concentrate here, Order-Dependent Mapping (ODM). We recall the basis of the method, for a class of series we give intuitive arguments to explain its convergence and illustrate its properties by several simple examples. Since the method was proposed, some rigorous convergence proofs were given. The method has also found a number of applications and we shall list a few.