Lagrange inversion

Lagrange inversion denotes a formula for the power series coefficients of the compositional inverse of an analytic function $f$ around $0$ satisfying $f(0)=0$, or of a formal power series in one or several variables.

Wikipedia: Lagrange inversion theorem, formal power series

Related entries: Faà di Bruno formula, noncommutative symmetric function, Lambert W-function

- I.M. Gessel,
*A noncommutative generalization and a $q$-analog of the Lagrange inversion formula*, Trans. Amer. Soc.**257**(1980), pp. 455–482,*A combinatorial proof of the multivariable Lagrange inversion formula*, J. Combin. Theory Ser. A**45**(1987), pp. 178–196 - Ira Gessel, Gilbert Labelle,
*Lagrange inversion for species*, J. Combin. Theory Ser. A 72 (1995), 95–117.

A homotopical algebra proof of the Lagrange inversion formula is exhibited in

- Vladimir Dotsenko,
*A Quillen adjunction between algebras and operads, Koszul duality, and the Lagrange inversion formula*, arxiv/1606.08222

There are relations to Faà di Bruno algebra:

- Christian Brouder, Alessandra Frabetti, Christian Krattenthaler,
*Non-commutative Hopf algebra of formal diffeomorphisms*, Adv. Math.**200**:2 (2006) 479-524 pdf - Jean-Paul Bultel,
*Combinatorial properties of the noncommutative Faà di Bruno algebra*, J. of Algebraic Combinatorics 38:243–273 (2013) MR3081645

An approach to Lagrange inversion using Heisenberg-Weyl algebra is in

- O. V. Viskov,
*A random walk with a skip-free component and the Lagrange inversion formula*, Theory Probab. Appl., 45(1), 164–172. (9 pages); O. V. Viskov,*Obrasčenie stepennyh rjadov i formula Lagranža*, Dokl. AN SSSR, 254:2 (1980) 269–271

category: analysis, combinatorics

Last revised on April 21, 2018 at 07:55:51. See the history of this page for a list of all contributions to it.