Contractive Laurent fractions and nested discs (Q1822703)

A Laurent fraction is a continued fraction \(K(a_ n(z)/b_ n(z))\) where \(a_ n(z)\) and \(b_ n(z)\) are certain Laurent polynomials of the form \(p_ nz^{-1}+q_ n+r_ nz\) for constants \(p_ n\), \(q_ n\), \(r_ n\). Certain circular disks are connected with the approximants of the Laurent fraction. These disks form, under certain circumstances, a sequence of nested circles and can therefore aid in questions of convergence and error estimates. Under special conditions so called generalized approximants are shown to have very simple partial fraction decompositions. The theorems are too complicated to quote here. The proofs employ information from a number of papers by the author and/or W. B. Jones and/or W. J. Thron.