Al-Salam and Verma introduced the class Sk of polynomial sets, and characterized such sets by their generating functions. Here we define a class Vk of sets of rank k by means of recurrence relations, and show that Sk ⊂ Vk; and we characterize those sets of Sk, and of Vk, that are orthogonal.
W. A. Al-Salam -A. Verma,Generalized Sheffer polynomials, Duke Math. J.,37, no. 2 (1970), pp. 361–365.
I. M. Sheffer,Some properties of polynomial sets of type zero, Duke Math. J.,5, no. 3 (1939), pp. 590–622.
Entrata in Redazione il 24 giugno 1977.
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Sheffer, I.M. On polynomial sets of classS k, and sets of rankk . Annali di Matematica 118, 295–324 (1978). https://doi.org/10.1007/BF02415133
- Generate Function
- Recurrence Relation