Some nonlinear inverse relations of Bell polynomials via the Lagrange inversion formula
Combinatorics
2021-02-09 v3
Abstract
In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula, J. Integer Seq., Vol. 22 (2019), Article 19.3.8. (https://cs.uwaterloo.ca/journals/JIS/VOL22/Wang/wang53.pdf). As applications of this inverse relation, we not only find a short proof of another nonlinear inverse relation due to Birmajer et al., but also set up a few convolution identities concerning the Mina polynomials.
Cite
@article{arxiv.2012.03412,
title = {Some nonlinear inverse relations of Bell polynomials via the Lagrange inversion formula},
author = {Jin Wang and Xinrong Ma},
journal= {arXiv preprint arXiv:2012.03412},
year = {2021}
}
Comments
22 pages