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Chebyshev polynomials and continued fractions related

Szczepański Jerzy

Science, Technology and Innovation

2019

Vol. 7, no. 4

1--8

Let p, q be complex polynomials, deg p>deg q ≥ 0. We consider the family of polynomials defined by the recurrence P_{n+1}=2pP_n-qP_{n-1) for n=1, 2, 3, ... with arbitrary P_1 and P_0 as well as the domain of the convergence of the infinite continued fraction f(z)=2p(z)-\cfrac{q(z)}{2p(z)-\cfrac{q(z)}{2p(z)-...

Diophantine approximations and almost periodic functions

Nawrocki A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

100--104

In this paper we investigate the asymptotic behaviour of the classical continuous and unbounded almost periodic function in the Lebesgue measure. Using diophantine approximations we show that this function can be estimated by functions of polynomial type and we give the best polynomial estimation.

On small vibrations of a damped Stieltjes string

Boyko O., Pivovarchik V.

Opuscula Mathematica

2015

Vol. 35, no. 2

143--159

Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses) is considered. For the case of point-wise damping at the first counting from the right end mass the problem of recovering the masses, the damping coefficient and the lengths of the subintervals by one spectrum and the total length of the string is solved.

q-Stern Polynomials as Numerators of Continued Fractions

Mansour T.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 1

11--18

We present a q-analogue for the fact that the nth Stern polynomial Bn(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. Moreover, we give a combinatorial interpretation for our q-analogue.