Abstract
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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Acknowledgements
The authors are indebted to the anonymous referees for many important suggestions leading to improvement of an earlier version of this paper. Thanks are also due to the organizers and the Program Committee of CM2021 for the chance to report our work and their recommendation to JSSC.
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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.
This paper was recommended for publication by Editor CHEN Shaoshi.
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Ma, X., Wang, J. Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (II). J Syst Sci Complex 36, 96–116 (2023). https://doi.org/10.1007/s11424-022-1300-8
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DOI: https://doi.org/10.1007/s11424-022-1300-8