zbMATH — the first resource for mathematics

On the Lagrange inversion formula. (Sur la formule d’inversion de Lagrange.) (French. English summary) Zbl 1129.13023
Summary: We extend the Lagrange inversion formula to the case of a commutative ring and series having some nilpotent terms in front of the term of degree 1. The method is purely algebraic.
13F25 Formal power series rings
05A15 Exact enumeration problems, generating functions
05A40 Umbral calculus
Full Text: DOI Numdam EuDML
[1] Barnabei (M.), Brini (A.), Nicoletti (G.).— Recursive matrices and umbral calculus. J. Algebra 75, p. 546-573 (1982). · Zbl 0509.05005
[2] Banderier (C.), Flajolet (P.).— Basic analytic combinatorics of directed lattice paths, Theor. Comput. Sci. 281, p. 37-80 (2002). · Zbl 0996.68126
[3] Comtet (L.).— Analyse combinatoire I et II, Presses Universitaires de France (1970). · Zbl 0221.05001
[4] Graham (R. L.), Knuth (D. E.), Patashnik (O.).— Concrete mathematics : a foundation for computer science, 2nd ed. Addison-Wesley (1994). · Zbl 0836.00001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.