Some systems of multivariable orthogonal q-Racah polynomials

Abstract

In 1991 Tratnik derived two systems of multivariable orthogonal Racah polynomials and considered their limit cases. q-Extensions of these systems are derived, yielding systems of multivariable orthogonal q-Racah polynomials, from which systems of multivariable orthogonal q-Hahn, dual q-Hahn, q-Krawtchouk, q-Meixner, and q-Charlier polynomials follow as special or limit cases.

Bispectral commuting difference operators for multivariable Askey-Wilson polynomials

“…In Section 2 we recall the basic definitions and orthogonal properties of the one-dimensional Askey-Wilson polynomials as well as the multivariable extension proposed by Gasper and Rahman. We also show that a change of variables leads to the multivariable q-Racah polynomials discussed in [7]. In Section 3 we define a q-difference operator L d acting on the variables z 1 , z 2 , .…”

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE qk-DIFFERENCE EQUATIONS

“…In recent years, the topic of q-calculus has attracted the attention of several researchers and a variety of new results can be found in the papers [1], [2], [3], [4], [5], [6], [8], [9], [10], [11], [12], [18], [19] and the references cited therein.…”

A study of second-order q-difference equations with boundary conditions

“…The study of q-difference equations, initiated in the beginning of the 20th century ( [1][2][3][4]), and, up to date, it has evolved into a multidisciplinary subject, (for example, see ( [5][6][7][8][9][10][11][12][13][14][15]) and references therein). For some recent work on q-difference equations, we refer the reader to the papers ( [16][17][18][19][20][21][22][23]). However, the theory of boundary value problems for nonlinear q-difference equations is still in the initial stage and many aspects of this theory need to be explored.…”