16 citations · 16 across the 2 of their papers we have counts for
6 papers
Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems
M. E. H. Ismail, S. S. Lin, S. S. Roan
In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin XXZ model of a finite size and the -Sturm-Liouville proble…
Generalizations of Chebyshev Polynomials and Polynomial Mappings
Y. Chen, J. C. Griffin, M. E. H. Ismail
We show how polynomial mappings of degree k from a union of disjoint intervals onto [-1,1] generate a countable number of special cases of a certain generalization of the Chebyshev…
q-Random Matrix Ensembles
K. A. Muttalib, Y. Chen, M. E. H. Ismail
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical system…
Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle
Mourad E. H. Ismail, Nicholas S. Witte
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and -difference equations for these polynomials. A gene…
Change of base in Bailey pairs
David Bressoud, Mourad Ismail, Dennis Stanton
Versions of Bailey's lemma which change the base from q to q^2 or q^3 are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities. We also…
Small eigenvalues of large Hankel matrices:The indeterminate case
Christian Berg, Yang Chen, Mourad E. H. Ismail
In this paper we characterise the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given…