Uniqueness of Padé approximants from series of orthogonal polynomials

Avram Sidi
1977 Mathematics of Computation  
It is proved that whenever a nonlinear Padé approximant, derived from a series of orthogonal polynomials, exists, it is unique. Let r(x), r = 0, 1, 2, ... , be a set of polynomials which are orthogonal on an interval [a, b], finite, semi-infinite, or infinite, with weight function w(x), whose integral over any subinterval of [a, b] is positive; i.e., r=m+n + l
doi:10.1090/s0025-5718-1977-0447901-1 fatcat:lyvma6j4wbbuvixr5z4dcxjpie