Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A new expression for umbral operators and power series inversion

Authors: A. M. Garsia and S. A. Joni
Journal: Proc. Amer. Math. Soc. 64 (1977), 179-185
MSC: Primary 05A10; Secondary 40A99
MathSciNet review: 0444487
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown here the compositional inversion of formal power series has a natural formulation in terms of umbral operators. This fact is used to derive a new proof of the Lagrange inversion theorem by operator theoretic methods.

References [Enhancements On Off] (What's this?)

  • [1] Adriano M. Garsia, An exposé of the Mullin-Rota theory of polynomials of binomial type, Linear and Multilinear Algebra 1 (1973), no. 1, 47–65. MR 0319779
  • [2] Ronald Mullin and Gian-Carlo Rota, On the foundations of combinatorial theory. III. Theory of binomial enumeration, Graph Theory and its Applications (Proc. Advanced Sem., Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1969) Academic Press, New York, 1970, pp. 167–213 (loose errata). MR 0274300

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A10, 40A99

Retrieve articles in all journals with MSC: 05A10, 40A99

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society