Pade Approximants, Their Properties, and Applications to Hydrodynamic Problems

This paper is devoted to an overview of the basic properties of the Pade transformation and its generalizations. The merits and limitations of the described approaches are discussed. Particular attention is paid to the application of Pade approximants in the mechanics of liquids and gases. One of the disadvantages of asymptotic methods is that the standard ansatz in the form of a power series in some parameter usually does not reflect the symmetry of the original problem. The search for asymptotic ansatzes that adequately take into account this symmetry has become one of the most important problems of asymptotic analysis. The most developed technique from this point of view is the Pade approximation.