Analysis and improvement of perturbation series
Abstract
Five examples of regular perturbation series are examined. The series had been obtained in connection with a variety of problems in the mechanics of viscous fluids. The nearest singularity is considered, taking into account the direction of the nearest singularity, its significance, the radius of convergence, the nature of the nearest singularity, an infinite radius of convergence, and a zero radius of convergence. Questions of an improvement of series with a nearest singularity on the positive axis are discussed along with the improvement of series with a nearest singularity off the positive axis.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 November 1974
 Bibcode:
 1974QJMAM..27..423V
 Keywords:

 Convergence;
 Fluid Mechanics;
 Perturbation Theory;
 Power Series;
 Singularity (Mathematics);
 Viscous Fluids;
 Approximation;
 Boundary Layer Flow;
 Error Analysis;
 Flow Resistance;
 Flow Theory;
 Stokes Flow;
 Viscous Flow;
 Physics (General)