nLab
umbral calculus

• wikipedia: umbral calculus
• eom: umbral calculus
• Steven M. Roman, Gian-Carlo Rota, Umbral calculus, Advances in Math. 27 (1978), no. 2, 95–188, pdf until p. 120, doi, MR0485417
• Nigel Ray, Universal constructions in umbral calculus, Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 343–357, Progr. Math. 161, Birkhäuser 1998, MR99e:05015, pdf, citeseer
• G.-C. Rota, B. D. Taylor, SIAM J. Math. Anal. 25 (1994), no. 2, 694–711; MR95d:05014, doi
• Thomas J. Robinson, Formal calculus and umbral calculus, The electronic journal of combinatorics 17 (2010), $\sharp R95$, pdf
• Doron Zeilberger, The umbral transfer-matrix method. I. Foundations.,

  In memory of Gian-Carlo Rota. J. Combin. Theory Ser. A 91 (2000), no. 1-2, 451–463, MR2001g:05018, doi

• A D Buchianico, D. Loeb, A selected survey of umbral calculus, pdf
• Li Guo, Baxter algebras and the umbral calculus, Adv. in Appl. Math. 27 (2001), 405-426; cf. also Rota-Baxter algebra