Limit relations involving 2-orthogonal polynomials

As an extension of the Askey-scheme, recently, it has been introduced the so-called d-Askey-scheme, which is a table describing families of hypergeometric d-orthogonal polynomials. In this paper, we derive limit relations linking between all levels of the 2-Askey-scheme (Figure 1). To this end, we use three methods. The first one is based on a recurrence relation. The second one uses difference and differential equations, and the third one deals with the hypergeometric expression of the considered polynomials. The recurrence relations, differential and difference equations will be determined by the use of Computer Algebra program Maple. That allows us to get, explicitly, the 2-Askey-scheme with various properties of their polynomials, which appears to be new.