Infinite product of power series
Kui-Yo Chen, Zhong-Tang Wu

TL;DR
This paper derives a universal formula for the coefficients of infinite products of power series with constant term 1, connecting partition and permutation structures, and unifying various binomial-type theorems.
Contribution
It introduces a new, universal coefficients formula for infinite power series products, linking partitions, permutations, and classical binomial theorems.
Findings
Provides an exact coefficients formula using partitions and permutations
Unifies multiple binomial-type theorems under a single framework
Offers new combinatorial interpretations for classical theorems
Abstract
We give an exact coefficients formula of any infinite product of power series with constant term equal to , by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type theorems in many sense. In particular, we give the new formulas as the double counting of Bell polynomial, Binomial Theorem and Multinomial Theorem.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematical functions and polynomials
