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

作者：MA Xinrong; WANG Jin^*

来源：Journal of Systems Science and Complexity, 2023, 36(01): 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.