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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…