ABSTRACT
The standard Padé approximant (PA) is an abundantly studied subject in the theory of rational approximations. This method is called the z-transform in engineering literature on signal processing. The PA is the most prominent member from the whole family of the known nonlinear sequence-to-sequence transformations. The overriding rationale for a firm establishment of the PA in physics is its mathematical equivalence with a number of the leading methods in quantum mechanics, e.g. Born’s perturbation expansions, finite-rank expansions with separable potential expansions, the Schwinger variational principles, the Green functions, the Fredholm determinants, etc. PA can resum wildly divergent series even with the zero convergence radius or if the coefficients grow as exponentials or factorials. Industrial companies in telephone communications are also interested in robust processing via PA i.e. the pole-zero modelling for applications in, e.g. effective speech coding, voice pattern recognition and verification, etc.
