The aim of this paper is to show the applications of the classical umbral calculus to the solution of difference equations in terms of Bernoulli umbrae [see G.-C. Rota and the author, SIAM J. Math. Anal. 25, No. 2, 694-711 (1994; Zbl 0797.05006)]. The primary application is to the Loeb-Rota algebra of logarithmic type power series [see D. E. Loeb and G.-C. Rota, Adv. Math. 75, No. 1, 1-118 (1989; Zbl 0688.05001)]. The others refer to the iterated process leading to Nörlund series and universal difference operators.
For the entire collection see [Zbl 0890.00032].