Direct and inverse results on row sequences of generalized Padé approximants to polynomial expansions

N. BosuwanSouth Carolina Commission on Higher EducationMahidol University2020-01-272020-01-272019-02-01Acta Mathematica Hungarica. Vol.157, No.1 (2019), 191-21915882632023652942-s2.0-85055729179https://repository.li.mahidol.ac.th/handle/20.500.14594/51231© 2018, Akadémiai Kiadó, Budapest, Hungary. Starting from the orthogonal and Faber polynomial expansions of a function F, we study the asymptotic behaviors of two generalized Padé approximations (orthogonal Padé approximation and Padé–Faber approximation). We obtain both direct and inverse results relating the convergence of the poles of these approximants and the singularities of F. Thereby, we obtain analogues of theorems by A. A. Gonchar and S. P. Suetin.Mahidol UniversityMathematicsDirect and inverse results on row sequences of generalized Padé approximants to polynomial expansionsArticleSCOPUS10.1007/s10474-018-0878-8