论文标题
通过Lagrange倒置公式的Bell多项式的一些非线性逆关系
Some nonlinear inverse relations of Bell polynomials via the Lagrange inversion formula
论文作者
论文摘要
在本文中，通过经典的拉格朗日反演公式，我们建立了一种一般的非线性逆关系，这是解决论文中提出的问题的部分解决方案[J. J. Wang，通过Lagrange倒置公式的Bell多项式的非线性逆关系，J。Integer Seq。，Vol。 22（2019），第19.3.8条。 （https://cs.uwaterloo.ca/journals/jis/vol22/wang/wang53.pdf）。作为这种反关系的应用，我们不仅找到了由于Birmajer等人而导致的另一个非线性逆关系的简短证明，而且还建立了与Mina多项式有关的一些卷积身份。
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.
