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math.CV2026
Analytic summation of series involving higher-order derivatives of Chebyshev polynomials of the second kind and their applications to convolved linear recurrent sequences
Dmitriy Dmitrishin, Daniel Gray, Vitaly Khamitov +1
This paper considers functional series whose terms are higher-order derivatives of Chebyshev polynomials of the second kind, where the degree of the polynomial is related to the or…
math.CV2026
Reciprocal Polynomials with Zeros on the Unit Circle and Derivatives of Chebyshev Polynomials of the Second Kind
Dmitriy Dmitrishin, Daniel Gray, Alexander Stokolos
In this article, we consider the reciprocal antisymmetric polynomial \[P(z) = \sum_{j = 0}^{s}(-1)^jγ_j\left(z^j - z^{N + s + 1 - j}\right), \ γ_0 = 1.\] It is shown that if all…
math.CV2025
Extremal polynomials for the Rogosinski--SzegÅ estimates of the third coefficient of nonnegative sine polynomials
Dmitriy Dmitrishin, Alexander Stokolos, Walter Trebels
In the class of normalized sine-polynomials non-negative on W.Rogosinski and G.SzegÅ 1950 considered a number of extremal problems and proved, among other things…