  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.
