Related papers: On coefficients of Yablonskii-Vorob'ev polynomial
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici \`a…
Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…
This paper mainly studies problems about so called "permutation polynomials modulo $m$", polynomials with integer coefficients that can induce bijections over Z_m={0,...,m-1}. The necessary and sufficient conditions of permutation…
We provide upper bounds on the degrees of the coefficients of \v{S}apovalov elements for a simple Lie algebra. If $\fg$ is a contragredient Lie superalgebra and $\gc$ is a positive isotropic root of $\fg,$ we prove the existence and…
We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formulas in their proof of the positivity results about these…
We obtain asymptotic formulas for sums over arithmetic progressions of coefficients of polynomials of the form $$\prod_{j=1}^n\prod_{k=1}^{p-1}(1-q^{pj-k})^s,$$ where $p$ is an odd prime and $n, s$ are positive integers. Let us denote by…
In this paper, we get the generating functions of q-Chebyshev polynomials using operator. Also considering explicit formulas of q-Chebyshev polynomials, we give new generalizations of q-Chebyshev polynomials called incomplete q-Chebyshev…
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
We investigate Chebyshev polynomials corresponding to Jacobi weights and determine monotonicity properties of their related Widom factors. This complements work by Bernstein from 1930-31 where the asymptotical behavior of the related…
We prove large sieve inequalities with multivariate polynomial moduli and deduce a general Bombieri--Vinogradov type theorem for a class of polynomial moduli having a sufficient number of variables compared to its degree. This sharpens…
In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…
The Jacobi polynomials on the simplex are orthogonal polynomials with respect to the weight function $W_\bg(x) = x_1^{\g_1} ... x_d^{\g_d} (1- |x|)^{\g_{d+1}}$ when all $\g_i > -1$ and they are eigenfunctions of a second order partial…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider a)the case when period $N$ of coefficients of recurrence…
The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on…
I study the Lyapunov exponent and the integrated density of states for general Jacobi operators. The main result is that questions about these, can be reduced to questions about ergodic Jacobi operators. Then, I apply this to $a(n) = 1$ and…
We introduce a theory of finite polynomial cohomology with coefficients in this paper. We prove several basic properties and introduce an Abel-Jacobi map with coefficients. As applications, we use such a cohomology theory to study…
We find a new formula for the orthonormal polynomials corresponding to a measure mu on the unit circle whose Verblunsky coefficients are periodic. The formula is presented using the Chebyshev polynomials of the second kind and the…