18 citations · 35 across the 9 of their papers we have counts for
10 papers
Orthogonal Polynomials of Askey-Wilson Type
Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou
We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of…
q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators
Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou
We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study…
Integrals and Series Representations of -Polynomials and Functions: Part II Schur Polynomials and the Rogers-Ramanujan Identities
Mourad E. H. Ismail, Ruiming Zhang
We give several expansion and identities involving the Ramanujan function and the Stieltjes--Wigert polynomials. Special values of our idenitities give -versions of some o…
Integral and Series Representations of -Polynomials and Functions: Part I
Mourad E. H. Ismail, Ruiming Zhang
By applying an integral representation for we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations…
-Bessel Functions and Rogers-Ramanujan Type Identities
Mourad E. H. Ismail, Ruiming Zhang
We evaluate -Bessel functions at an infinite sequence of points and introduce a generalization of the Ramanujan function and give an extension of the -version of the Rogers-R…
Kibble-Slepian Formula and Generating Functions for 2 Polynomials
Mourad E. H. Ismail, Ruiming Zhang
We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the D Hermite polynomials recently proved in \cite{Ism4}. W…