Spurious poles in Padé approximation (Q1298590)

The author observes that the spurious poles, the non controled poles of Padé approximants, depend in fact on properties of the orthogonality relations defining the denominators of Padé approximants. The position of these poles, which do not correspond to analytic properties of the approximated function \(f\), is studied and some new ideas to understand this difficult problem are proposed.