Partition-theoretic Frobenius-type limit formulas
Document Type
Article
Publication Date
1-1-2024
Abstract
Using partition generating function techniques, we prove q-series analogues of a formula of Frobenius generalizing Abel’s convergence theorem for complex power series. Frobenius’ result states that for | q |< 1 , limq → 1 ( 1-q ) ∑ n ≥ 1 f ( n )qn is equal to the average value lim N → ∞ 1 N ∑ k = 1 N f ( k ) of the sequence { f ( n ) } as n → ∞ , if the average value exists.
Publication Title
Ramanujan Journal
Recommended Citation
Schneider, R.
(2024).
Partition-theoretic Frobenius-type limit formulas.
Ramanujan Journal.
http://doi.org/10.1007/s11139-024-00835-4
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/711
