Related papers: An orthogonal polynomial coefficient formula for t…
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…
We give simple new proofs of some Hankel determinant evaluations by Omer Egecioglu and Aleksandar Cvetkovic, Predrag Rajkovic and Milos Ivkovic and prove analogous results for sums of moments of symmetric orthogonal polynomials.
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the…
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…
It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to $q$-binomial transforms and study the behavior of the…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
The usual implement procedure for the reconstruction of secular equation for an effective Hamiltonian has been discussed and improved. A relative characteristic polynomial has been introduced for the effective Hamiltonian, to obtain a…
We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…
The derivation of zonal polynomials involves evaluating the integral \[ \exp\left( - \frac{1}{2} \operatorname{tr} D_{\beta} Q D_{l} Q \right) \] with respect to orthogonal matrices \(Q\), where \(D_{\beta}\) and \(D_{l}\) are diagonal…
In recent years, chain sequences and their perturbations have played a significant role in characterising the orthogonal polynomials both on the real line as well as on the unit circle. In this note, a particular disturbance of the chain…
We extend the well-known Melzak binomial transform formula to polynomials of any degree and show some applications.
We present an explicit branching formula for the six-parameter Macdonald-Koornwinder polynomials with hyperoctahedral symmetry.
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
We obtain an extension of the Christoffel--Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.
In this paper we introduce and discuss some classes of orthogonal polynomials in several non-commuting variables. The emphasis is on a non-commutative version of the orthogonal polynomials on the real line. We introduce recurrence equations…
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and then we obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace…
A characterization is given of those sequences of quasi-orthogonal polynomials which form also $q$-Appell sets.