Self-similarly corrected Pade approximants for the indeterminate problem

A method is suggested for treating the well-known deficiency in the use of Pade approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of self-similarly corrected Pade approximants, making it possible to essentially increase the class of functions treated by these approximants. The method works well even in those cases where the standard Pade approximants are not applicable, resulting in divergent sequences. Numerical convergence of our method is demonstrated by several physical examples.