Double affine Hecke algebras of rank 1 and the -symmetric Askey-Wilson relations.
Doubles mélanges des polylogarithmes multiples aux racines de l’unité
Dual pairs, spherical harmonics and a Capelli identity in quantum group theory
Duality of -polynomials, orthogonal on countable sets of points.
Dunkl operators
Dynamical matrices of elliptic quantum groups and connection matrices for the -KZ equations.
Enumeration of sequences constrained by the ratio of consecutive parts.
Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equations
Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J
We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations as single...
Expectation of Random Polytopes.
Extensions of Bailey's transform and applications.
Finite Rogers-Ramanujan type identities.
Fractional quantum integral inequalities.
From double Hecke algebra to analysis.
Fuchsian differential equation for the perimeter generating function of three-choice polygons.
Generalization of some inequalities for the gamma function.
Generalization of some inequalities for the -gamma function.
Generalization of two identities in Ramanujan's lost notebook
Generalizations of Milne’s -Chu-Vandermonde summation
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...
Generalized coherent states for -oscillator associated with discrete -Hermite polynomials.