Year: 2026
Type: preprint
Abstract: If $\boldsymbol{w} = (w_1,w_2,\dots)$ is a sequence in $\mathbb{N}=\{1,2,\dots\}$, the partial Bell polynomials based on $\boldsymbol{w}$ are $B_{n,k}$ for $k \in \mathbb{N}$ and $n\in\{k,k+1,\dots\}$. Let $F(z) = \sum_{n=1}^{\infty} (w_n/n!)z^n$ be the exponential generating function for $\boldsymbol{w}$, and assume the radius of convegence is positive $R>0$. Then $F(z)^k = \sum_{n=k}^{\infty} (k!/n!) z^n B_{n,k}$ for $|z|
Source: arXiv (Cornell University)
Authors: Li, Sophia, Starr, Shannon
Institution: University of Alabama at Birmingham
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212043198
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