9 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…
An extremal problem for odd univalent polynomials
Dmitriy Dmitrishin, Daniel Gray, Alexander Stokolos +1
For the univalent polynomials with real coefficients and normalization \(a_1 = 1\) we solve the extremal problem \[ \min_{a_j:\,a_1=1} \…
Koebe's theorem for trinomials with fold symmetry
Dmitriy Dmitrishin, Daniel Gray, Alexander Stokolos
The Koebe problem for univalent polynomials with real coefficients is fully solved only for trinomials, which means that in this case the Koebe radius and the extremal polynomial (…
Extremal problems for trinomials with fold symmetry
Dmitriy Dmitrishin, Alex Stokolos, Daniel Gray
The famous T. Suffridge polynomials have many extremal properties: the maximality of coefficients when the leading coefficient is maximal; the zeros of the derivative are located o…