Catalan numbers revisited (Q5902927)

Motivated by author's earlier development of binomial functions [ibid. 70, 460-473 (1979; Zbl 0416.05007); ibid. 83, 110-125 (1981; Zbl 0477.05004)] the notion of Catalan binomial functions, Catalan matrices and that of Sheffer functions is introduced as a generalization of the same named sequences. A variety of combinatorial identities is proved and some applications are outlined (e.g. to the inverse Laplace transform).