§18.21 Hahn Class: Interrelations

§18.21(i) Dualities

¶ Duality of Hahn and Dual Hahn

For the dual Hahn polynomial see §18.25.

§18.21(ii) Limit Relations and Special Cases

¶ Meixner–Pollaczek Laguerre

A graphical representation of limits in §§18.7(iii), 18.21(ii), and 18.26(ii) is provided by the Askey scheme depicted in Figure 18.21.1.

Figure 18.21.1: Askey scheme. The number of free real parameters is zero for Hermite polynomials. It increases by one for each row ascended in the scheme, culminating with four free real parameters for the Wilson and Racah polynomials. (This is with the convention that the real and imaginary parts of the parameters are counted separately in the case of the continuous Hahn polynomials.)