Partition-theoretic Frobenius-type Limit Formulas

Authors

Robert Schneider, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

4-12-2024

Department

Department of Mathematical Sciences

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 , lim_{q → 1}(1―q) ∑_n≥1 f(n)qⁿ is equal to the average value lim_{N → ∞} 1/ N ∑ ^N_{k = 1} 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, 65, 1941-1948. http://doi.org/10.1007/s11139-024-00835-4
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/711