On the q-factorization of power series
Document Type
Article
Publication Date
6-21-2025
Department
Department of Mathematical Sciences
Abstract
Any power series with unit constant term can be factored into an infinite product of the form ∏n≥1(1-qn)-an. We give direct formulas for the exponents an in terms of the coefficients of the power series, and vice versa, as sums over partitions. As examples, we prove identities for certain partition enumeration functions. Finally, we note q-analogues of our enumeration formulas.
Publication Title
Ramanujan Journal
Recommended Citation
Schneider, R.,
Sills, A.,
&
Waldron, H.
(2025).
On the q-factorization of power series.
Ramanujan Journal,
67(4).
http://doi.org/10.1007/s11139-025-01140-4
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1774