Some nonlinear inverse relations of Bell polynomials via the Lagrange inversion formula

2020/12/07 by Jin Wang, Wang, Jin, Xinrong Ma +1
Chemistry · Mathematics · #05A10 #05A19 #11B83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.2012.03412

openalex publication_date 2020/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A fast algorithm for computing Bell polynomials based on index\n break-downs using prime factorization

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