Related papers: A simple approach to some Hankel determinants
After a short survey about Schroeder numbers and some generalizations which I call Schroeder-like numbers I study some q-analogues which have simple Hankel determinants.
We give simple proofs for the Hankel determinants of q-exponential polynomials.
Recently I. Mezo studied a simple but interesting generalization of the exponential polynomials. In this note I consider two q-analogues of these polynomials and compute their Hankel determinants.
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
In this (mostly expository) paper I want to share some observations prompted by a class of matrices whose determinants are Catalan numbers. Considering different methods of proof we obtain some generalizations and q-analogues and…
In this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers. Here we consider $\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a…
In this note we show that various natural q-analogues of the Catalan numbers can be obtained in a uniform way. Furthermore we compute their Hankel determinants.
We give a simple proof of the so called reproducing kernel thesis for Hankel operators
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
This note presents some results about Hankel determinants of backwards shifted Catalan-like numbers and related sequences.
We present a simple approach to discrete q-Hermite polynomials with special emphasis on analogies with the classical case.
The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval.The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics…
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 (partly expository) paper we give a short overview about the close relationship between the sequence of Catalan numbers and Hankel determinants from the point of view of orthogonal polynomials and show that an analogous situation…
Applying Johann Cigler's Hankel determinant formula in terms of the binomial coefficient determinants, which is simplified from Christian Krattenthale's, we get an explicit formula of Hankel determinants for general. As far as I know, those…
In this paper we introduce a class of determinants "of Hankel type". We use them to compute certain remarkable families of Drinfeld quasi-modular forms.
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 give an overview of known results about Hilbert matrices from the point of view of orthogonal polynomials and compute Hankel determinants of harmonic numbers and related topics.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
In this note, we present the determinant, the inverse and a lower bound for the smallest eigenvalue for some Hankel matrices