Operator Methods and Lagrange Inversion: A Unified Approach to Lagrange Formulas
Open Access
- 1 February 1988
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 305 (2) , 431-465
- https://doi.org/10.2307/2000874
Abstract
We present a general method of proving Lagrange inversion formulas and give new proofs of the -variable Lagrange-Good formula [13] and the -Lagrange formulas of Garsia [7], Gessel [10], Gessel and Stanton [11, 12] and the author [18]. We also give some -analogues of the Lagrange formula in several variables.Keywords
This publication has 18 references indexed in Scilit:
- Another family of q-Lagrange inversion formulasRocky Mountain Journal of Mathematics, 1986
- Aq-analog of the Lagrange expansionArchiv der Mathematik, 1984
- Higher dimensional recursive matrices and diagonal delta sets of seriesJournal of Combinatorial Theory, Series A, 1984
- A New q-Lagrange Formula and some ApplicationsProceedings of the American Mathematical Society, 1984
- Recurrence relations, continued fractions, and orthogonal polynomialsMemoirs of the American Mathematical Society, 1984
- A Noncommutative Generalization and q-Analog of the Lagrange Inversion FormulaTransactions of the American Mathematical Society, 1980
- Operatormethoden fürq-IdentitätenMonatshefte für Mathematik, 1979
- A New Expression for Umbral Operators and Power Series InversionProceedings of the American Mathematical Society, 1977
- Combinatorial IdentitiesMathematics of Computation, 1969
- Generalizations to several variables of Lagrange's expansion, with applications to stochastic processesMathematical Proceedings of the Cambridge Philosophical Society, 1960