-Bernstein polynomials associated with -Stirling numbers and Carlitz's -Bernoulli numbers.
-classical orthogonal polynomials: A very classical approach.
-Genocchi numbers and polynomials associated with -Genocchi-type -functions.
-orthogonal polynomials related to the quantum group .
-Riemann zeta function.
-Selberg integrals and Macdonald polynomials
q-Heat Operator and q-Poisson’s Operator
2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated with the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhi and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part, we introduce the q-Poisson operator P^t, and address its main properties. We show...
Quantum algebras and associated with certain -Hahn polynomials: a revisited approach.
Quantum Barnes function as the partition function of the resolved conifold.
Quelques valeurs prises par les polynômes de Macdonald décalés
Nous explicitons la valeur de certains des coefficients binomiaux généralisés associés aux polynômes de Macdonald, c’est-à-dire la valeur en certains points particuliers des polynômes de Macdonald décalés. Ces expressions font intervenir les fonctions hypergéométriques de base .
Raising and lowering operators for Askey-Wilson polynomials.
Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
Representations of the quantum algebra and discrete -ultraspherical polynomials.
Riesz potentials derived by one-mode interacting Fock space approach
The main aim of this short paper is to study Riesz potentials on one-mode interacting Fock spaces equipped with deformed annihilation, creation, and neutral operators with constants and , as in equations (1.4)-(1.6). First, to emphasize the importance of these constants, we summarize our previous results on the Hilbert space of analytic L² functions with respect to a probability measure on ℂ. Then we consider the Riesz kernels of order 2α, , on ℂ if , which can be derived from the Bessel...
Riordan arrays, Sheffer sequences and “orthogonal” polynomials.
Rogers-Ramanujan-Slater type identities.
Self-conjugate vector partitions and the parity of the spt-function
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...
Septic analogues of the Rogers-Ramanujan functions
Septic theta function identities in Ramanujan's lost notebook