On zeros of numerator and denominator polynomials of Thiele’s continued fraction - Pahirya, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.518:519.652We 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 established that the convergents of Thiele’s continued fraction form a staircase sequence of normal Pad´e approximants. The region of zeros of the denominator polynomial of the convergent of Thiele’s continued fraction is also determined.