Invariance properties in Hermite-Padé approximation theory

摘要

The Padé approximant is invariant under both linear fractional transformations of the function value and linear fractional transformations (origin fixed) of the argument. The paper reports on an investigation of these invariance properties to the class of Hermite-Padé approximants based on the class of general ordinary nonlinear differential equations. Further, the paper characterizes the class with these invariance properties. Uniqueness is discussed. Examples are given, such as the Padé-Riccati approximants, and allowed types of singular points are discussed.