Related papers: Hankel determinants of Schroeder-like numbers
It is shown that some q-analogues of the Fibonacci and Lucas polynomials lead to q-analogues of the Chebyshev polynomials which retain most of their elementary properties.
In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
This note collects some facts and conjectures about the Hankel determinants and their generating functions of the columns of Hoggatt triangles which apparently are related to combinatorial objects such as Young tableaux and Narayana…
We prove and generalize a conjecture of Johann Cigler on the Hankel determinants of convolution powers of Narayana polynomials. Our method follows a "guess-and-prove" strategy, relying on established techniques involving Hankel continued…
In this paper we establish several relations between the determinants of the following structured matrices: Hankel matrices, symmetric Toeplitz + Hankel matrices and Toeplitz matrices. Using known results for the asymptotic behavior of…
We evaluate the Hankel determinants of the convolution powers of Motzkin numbers for $r\leq 27$ by finding shifted periodic continued fractions, which arose in application of Sulanke and Xin's continued fraction method. We also conjecture…
We solve the connection coefficient problem between the Al-Salam-Chihara polynomials and the q-Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some…
We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.
In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.
We study the Hankel transforms of sequences related to the central coefficients of a family of Pascal-like triangles. The mechanism of Riordan arrays is used to elucidate the structure of these transforms.
The Euler numbers occur in the Taylor expansion of $\tan(x)+\sec(x)$. Since Stieltjes, continued fractions and Hankel determinants of the even Euler numbers, on the one hand, of the odd Euler numbers, on the other hand, have been widely…
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.
We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.
Orthogonal q-polynomials associated with q-Laguerre-Hahn form will be studied as a generalization of the q-semiclassical forms via a suitable q-difference equation. The concept of class and a criterion to determinate it will be given. The…
The classical $q$-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give $q$-analogues of rational numbers. Some combinatorial interpretations are already known, namely as the rank generating functions for…
I present a $q$-analog of the discrete Painlev\'e I equation, and a special realization of it in terms of $q$-orthogonal polynomials.