Expansion formulas. II. Variations on a theme

AbstractIn “Expansion Formulas, I” [S. A. Joni, J. Math. Anal. Appl. 81 (1981)], it was shown that the Steffensen formula or polynomial sequences of binomial type gives rise to a method for generating a certain class of expansion identities. Special cases of this class of identities were studied by Carlitz [SIAM J. Appl. Math. 26 (1974), 431–436; 8 (1977), 320–336]. Since the Umbral calculus for polynomial sequences of binomial type has been generalized to encompass the theories of composition sequences [A. M. Garsia and S. A. Joni, Comm. Algebra, in press] and factor sequences [S. Roman and G.-C. Rota, Adv. in Math. 27 (1978), 95–188], we herein extend the results of part I to these two more general settings