On Zeros of the Numerator and Denominator Polynomials of Thiele's Continued Fraction

Abstract

We prove that the polynomials of canonical numerators and denominators of the interpolation and approximation convergents of Thiele's continued fractions have no common zeros. It is shown that the convergents of Thiele's continued fraction form a staircase sequence of normal Pade approximants. The region containing zeros of the denominator polynomial of the convergent of Thiele's continued fraction is also determined.