Séries de -factorielles, opérateurs aux -différences et confluence
Several -series identities from the Euler expansions of and
In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two -series identities obtained by the Euler expansions of and . Several -series identities are obtained involving a -series identity in Ramanujan’s Lost Notebook.
Signed words and permutations. III: The MacMahon Verfahren.
Some biorthogonal -polynomials in two variables.
Some conjectures for Macdonald polynomials of type .
Some explicit values for ratios of theta-functions.
Some inequalities for the -digamma function.
Some new Formulas involving Functions
Some new transformations for Bailey pairs and WP-Bailey pairs
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.
Some recurrence relations for the generalized basic hypergeometric functions.
Some relationships between the analogs of Euler numbers and polynomials.
Some theorems on the explicit evaluations of singular moduli.
Spherical functions on a complex classical quantum group
Spherical functions on a family of quantum 3-spheres
Supernomial coefficients, supernomials coefficients Bailey's lemma and Rogers-Ramanujan-type identities. A survey of results and open problems.
Symmetric functions and multivariate basic hypergeometric series. (Fonctions symétriques et séries hypergéométriques basiques multivariées.)
Systèmes aux -différences singuliers réguliers : classification, matrice de connexion et monodromie
G.D. Birkhoff a posé, par analogie avec le cas classique des équations différentielles, le problème de Riemann-Hilbert pour les systèmes “fuchsiens” aux -différences linéaires, à coefficients rationnels. Il l’a résolu dans le cas générique: l’objet classifiant qu’il introduit est constitué de la matrice de connexion et des exposants en et . Nous reprenons sa méthode dans le cas général, mais en traitant symétriquement et et sans recours à des solutions à croissance “sauvage”. Lorsque ...
The Bergman kernel: Explicit formulas, deflation, Lu Qi-Keng problem and Jacobi polynomials
We investigate the Bergman kernel function for the intersection of two complex ellipsoids We also compute the kernel function for and show deflation type identity between these two domains. Moreover in the case that we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem.
The combinatorics of the Al-Salam-Chihara -Charlier polynomials.
The dynamical quantum group.