Some systems of multivariable orthogonal q-Racah polynomials

Some Systems of Multivariable Orthogonal Askey-wilson Polynomials

X iv :m at h/ 04 10 24 9v 1 [ m at h. C A ] 1 0 O ct 2 00 4 Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials George Gasper* and Mizan Rahman† Abstract In 1991 Tratnik derived two systems of multivariable orthogonal Wilson polynomials and considered their limit cases. q-Analogues of these systems are derived, yielding systems of multivariable orthogonal Askey-Wilson polynomials ...

Bispectrality of Multivariable Racah-wilson Polynomials

We construct a commutative algebra Ax of difference operators in R, depending on p + 3 parameters which is diagonalized by the multivariable Racah polynomials Rp(n; x) considered by Tratnik [27]. It is shown that for specific values of the variables x = (x1, x2, . . . , xp) there is a hidden duality between n and x. Analytic continuation allows us to construct another commutative algebra An in ...

The q-Racah-Krall-type polynomials

Frequency domain identification of multivariable systems using vector orthogonal polynomials

Frequency domain methods are known to suffer from a poor numerical conditioning when the frequency span and/or the model order become large (more than two decades and an order larger than twenty). This numerical problem destroys both the modeling performance and the model order selection capability. This paper presents a modeling approach that leads to (almost) optimal numerical conditioning of...

On some properties of q-Hahn multiple orthogonal polynomials

This contribution deals with multiple orthogonal polynomials of type II with respect to q-discrete measures (q-Hahn measures). In addition, we show that this family of multiple orthogonal polynomials has a lowering operator, and raising operators as well as a Rodrigues type formula. The combination of lowering and raising operators leads to a third order q-difference equation when two orthogona...