14 citations · 43 across the 23 of their papers we have counts for
27 papers
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…
Convolved Numbers of -sections of the Fibonacci Sequence: Properties, Consequences
Vitaly M. Khamitov, Dmitriy Dmitrishin, Alexander Stokolos +1
One possible data encryption scheme is related to stream ciphers, which use a sufficiently long pseudo-random sequence. To increase the cryptographic strength of the cipher, linear…
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 th…
Extremal polynomials for the Rogosinski--Szegő 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.Szegő 1950 considered a number of extremal problems and proved, among other things,…
Some properties of the quadrinomials and
Dmitriy Dmitrishin, Alexander Stokolos
We show that all the zeros of the quadrinomial lie on the unit circle if and only if the inequalities \[ -1\leκ\le 1\; (\mbox{ if is even}),\;\; -1\le…
Extremizers for the Rogosinski-Szegö estimate of the second coefficient in nonnegative sine polynomials
Dmitriy Dmitrishin, Alexander Stokolos, Walter Trebels
For the class of sine polynomials which are nonnegative on , W. Rogosinski and G. Szegö derived, among other things, ex…