Location and structure of the nearest singularity of a perturbation series

Abstract

The incompressible potential flow over a perturbed body is used as a model to shed light into the nature of the nearest singularity of a perturbation series. The solutions for various physical quantities are developed as a formal perturbation expansion in powers of a parameter up to 30 terms. The tedious computation is relegated to a computer. The calculations reveal that the location and structure of the nearest singularity of a pertubation series do change with the field point at the which the series is evaluated. Also the radius of convergence and behaviour of the perturbation series do depend significantly on the choice of the physical quantities. These results may provide salutary information for the analysis of computer extended pertubation series.