### Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (II)

MA Xinrong1, WANG Jin2

1. 1. Department of Mathematics, Soochow University, Suzhou 215006, China;
2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
• Received:2021-08-15 Revised:2021-11-17 Online:2023-01-25 Published:2023-02-09
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 11971341 and 12001492, and the Natural Science Foundation of Zhejiang Province under Grant No. LQ20A010004.

MA Xinrong, WANG Jin. Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (II)[J]. Journal of Systems Science and Complexity, 2023, 36(1): 96-116.

In this paper, by means of the classical Lagrange inversion formula, the authors establish a general nonlinear inverse relation as the 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]. As applications of this inverse relation, the authors not only find a short proof of another nonlinear inverse relation due to Birmajer, et al. (2012), but also set up a few convolution identities concerning the Mina polynomials.
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