Petro Kolosov

collaborators

3 papers

math.GM2021

An unusual identity for odd-powers

Petro Kolosov

In this manuscript we provide a new polynomial pattern. This pattern allows to find a polynomial expansion of the form \[x^{2m+1} = \sum_{k=1}^{x}\sum_{r=0}^{m} \mathbf{A}_{m,r} k^…

math.CA2016

A study on partial dynamic equation on time scales involving derivatives of polynomials

Petro Kolosov

Let $P (m, b, x)$ be a $2 m + 1$ -degree polynomial in $x, b$ . Let be a two-dimensional timescale $Λ^2 = \mathbb{T}_1 \times \mathbb{T}_2 = \{t=(x, b) \colon \; x\in\mathbb{T}_1, \; b\in\m…

math.NT2016

On the link between binomial theorem and discrete convolution

Petro Kolosov

Let $P_{b}^{m} (x)$ be a $2 m + 1$ -degree polynomial in $x$ and $b \in R$ \[ \mathbf{P}^{m}_{b}(x) = \sum_{k=0}^{b-1} \sum_{r=0}^{m} \mathbf{A}_{m,r} k^r (x-k)^r \] w…