# §18.26 Wilson Class: Continued

## §18.26(i) Representations as Generalized Hypergeometric Functions

For the definition of generalized hypergeometric functions see §16.2.

## §18.26(iii) Difference Relations

For comments on the use of the forward-difference operator , the backward-difference operator , and the central-difference operator , see §18.2(ii).

For each family only the -difference that lowers is given. See Koekoek et al. (2010, Chapter 1) for further formulas.

## §18.26(iv) Generating Functions

For the hypergeometric function see §§15.1 and 15.2(i).

## §18.26(v) Asymptotic Approximations

For asymptotic expansions of Wilson polynomials of large degree see Wilson (1991), and for asymptotic approximations to their largest zeros see Chen and Ismail (1998).

Koornwinder (2009) rescales and reparametrizes Racah polynomials and Wilson polynomials in such a way that they are continuous in their four parameters, provided that these parameters are nonnegative. Moreover, if one or more of the new parameters becomes zero, then the polynomial descends to a lower family in the Askey scheme.