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. Di Bucchianico, D. Loeb, A selected survey of umbral calculus. Electronic Journal of Combinatorics 2 (1995), 28, pdf
Li Guo, Baxter algebras and the umbral calculus, Adv. in Appl. Math. 27 (2001), 405-426; cf. also Rota-Baxter algebra
G. Dattoli, E. Palma, , E. Sabia, K. Górska, A. Horzela, K. A. Penson, Operational versus umbral methods and the Borel transform, Int. J. Appl. Comput. Math (2017) 3: 3489 doi

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