Related papers: q-Abel polynomials
In this work, we are interested by the $q$-Bessel Fourier transform with a new approach. Many important results of this $q$-integral transform are proved with a new constructive demonstrations and we establish in particular the associated…
We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference…
Three $q$-versions of Lommel polynomials are studied. Included are explicit representations, recurrences, continued fractions, and connections to associated Askey--Wilson polynomials. Combinatorial results are emphasized, including a…
From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.
In this note, we prove some combinatorial identities and obtain a simple form of the eigenvalues of $q$-Kneser graphs.
This is an informal and mostly expository note describing some asymptotic behavior and qualitative properties of the q-binomial coefficients. The results are mostly not new, but the overall story we present does not seem to be well known --…
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.
The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
This work makes a parallel construction for curves on threefolds to a ``current-theoretic'' proof of Abel's theorem giving the rational equivalence of divisors P and Q on a Riemann surface when Q - P is (equivalent to) zero in the Jacobian…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.
We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.
We introduce a $q$-analog of the polyanalytic Bargmann transform on $\mathbb{C}$.
Using the methodology of (rigorous) {\it experimental mathematics}, we give a simple and motivated solution to Zudilin's question concerning a $q$-analog of a problem posed by Asmus Schmidt about a certain binomial coefficients sum. Our…
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
A brief and elementary introduction to the subject is presented. Two open problems are given.
A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little…
We establish $q$-analogs for four congruences involving central binomial coefficients. The $q$-identities necessary for this purpose are shown via the $q$-WZ method.
We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This…
We have introduced q-analogues of bounded symmetric domains in our work q-alg/9703005. Given the simplest ones among those, the works q-alg/9603012 and math.QA/9803110 announce the relations describing the algebras of functions,…