Anatomy of a q-generalization of the Laguerre/Hermite Orthogonal Polynomials

2016/12/29 by Chan, Chuan-Tsung, Liu, Hsiao-Fan
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1612.09039

Abstract

We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the Heisenberg algebra, and the Hankel determinants. The power of quadratic relation is illustrated by comparing two ways of calculating recursive coefficients. Finally, we derive a q-deformed version of the Toda equations for both q-Laguerre/Hermite ensembles.

Related

• Matrix-Valued Hermite and Laguerre polynomials via Quadratic Transformation
• Orthogonality of a new family of q-Sobolev type polynomials
• q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations
• On some 2D orthogonal q-polynomials
• Three types of polynomials related to q-oscillator algebra