-species and the -Mehler formula.
A family of tridiagonal pairs related to the quantum affine algebra .
A new generating function of (-) Bernstein-type polynomials and their interpolation function.
A note on -partial difference equations and some applications to generating functions and -integrals
We study the condition on expanding an analytic several variables function in terms of products of the homogeneous generalized Al-Salam-Carlitz polynomials. As applications, we deduce bilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. We also gain multilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. Moreover, we obtain generalizations of Andrews-Askey integrals and Ramanujan -beta integrals. At last, we derive ...
A note on the modified -Bernstein polynomials.
A note on the -Euler measures.
A recovery of Brouncker's proof for the quadrature continued fraction.
350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/π. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his Arithmetica Infinitorum. We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's...
A study of -Laguerre polynomials through the -operator
The present paper deals with certain generating functions and recurrence relations for -Laguerre polynomials through the use of the -operator introduced in an earlier paper [7].
Affine transformations of a Leonard pair.
An algebra of integral operators.
An inequality for Chebyshev connection coefficients.
Double affine Hecke algebras of rank 1 and the -symmetric Askey-Wilson relations.
Duality of -polynomials, orthogonal on countable sets of points.
Generalized coherent states for -oscillator associated with discrete -Hermite polynomials.
Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra
Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.
Inequalities for the smallest zeros of Laguerre polynomials and their -analogues.
Irrationality proof of a q-extension of ζ(2) using little q-Jacobi polynomials
Nonnegative linearization of orthogonal polynomials
On bounds for the characteristic functions of some degenerate multidimensional distributions.
On orthogonality relations for dual discrete -ultraspherical polynomials.