Ruiming Zhang

On the Hellmann-Feynman theorem and the variation of zeros of certain special functions

We present a precise formulation and a rigorous proof of the Hellmann-Feyrunan theorem of quantum chemistry. We mention some applications of this theorem to studying monotonicity properties of zeros of special functions and orthogonal polynomials.

Chaotic and Periodic Asymptotics for q-Orthogonal Polynomials

We derive Plancherel-Rotach asymptotic expansions for the q �1 -Hermite, q-Laguerre, and Stieltjes-Wigert polynomials using a discrete analogue of Laplace’s method. The asymptotics in the bulk exhibit chaotic behavior when a certain variable is irrational. In the rational case, the main terms in the asymptotic expansion involve theta functions.

Kibble-Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the

Classes of Bivariate Orthogonal Polynomials

2

New Proofs of Some q-Series Results

D Hermite polynomials recently proved in \cite{Ism4}. We derive integral representations for the

Integral and series representations of q-polynomials and functions: Part I

2

PAGES FROM THE COMPUTER FILES OF R. WILLIAM GOSPER

D Hermite polynomials which are of independent interest. Several new generating functions for

Diagonalization of Certain Integral Operators

2

On some strange summation formulas

D

On some 2 orthogonal -polynomials

q