Про нулі многочленів чисельника та знаменника ланцюгового дробу Тіле

M. M. Pahirya

doi:10.37863/umzh.v74i1.6133

M. M. Pahirya Uzhhorod National University https://orcid.org/0000-0003-1488-3302

DOI: https://doi.org/10.37863/umzh.v74i1.6133

Abstract

UDC 517.518:519.652

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 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.

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On zeros of numerator and denominator polynomials of Thiele’s continued fraction

Abstract

References