We determine the q-orthogonal polynomial solutions to the difference equation DqPn(X) = γnPn-1(X), where Dq is the Askey-Wilson divided-difference operator, using an approach that does not appear in the literature. To accomplish this, we construct a polynomial expansion via a Chebyshev basis, which ultimately allows explicit formulas to be derived for the recurrence coefficients of Pn(X) above. From there, we obtain our solutions and discuss some future research.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics