Inverse polynomial expansions of Laurent series, II

Inverse polynomial expansions of Laurent series, II

An algorithm is considered, and shown to lead to various unusual and unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by the rational functions which are the partial sums of these series are investigated. The types of series corresponding to rational functions themselves are also partially characterized.

Metric Properties of Engel Series Expansions of Laurent Series

Modeling Potential Flow Using Laurent Series Expansions and Boundary Elements

The fundamental underpinnings of the well-known Bernoulli’s Equation, as used to describe steady state two-dimensional flow of an ideal incompressible irrotational flow, are typically described in terms of partial differential equations. However, it has been shown that the Cauchy Integral Theorem of standard complex variables also explain the Bernoulli’s Equation and, hence, can be directly use...

Laurent Polynomial Inverse Matrices and Multidimensional Perfect Reconstruction Systems

We study the invertibility of M -variate polynomial (respectively : Laurent polynomial) matrices of size N by P . Such matrices represent multidimensional systems in various settings including filter banks, multipleinput multiple-output systems, and multirate systems. Given an N × P polynomial matrix H(z) of degree at most k, we want to find a P × N polynomial (resp. : Laurent polynomial) left ...

Polynomial Expansions

The expansion of arbitrary power series in various classes of polynomial sets is considered. Some applications are also given. Notations. We will use the following contracted notation for the generalized hypergeometric function •i> •flB P q\bl,...,bQ pFAb, ^ M* z_k where p. « r(o4 k) («iOfc-n fy)*. (*v*s rw* and (°)* / = ! / = ! r(o)