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≥1f(n)qn is equal to the average value limN→∞1N∑k=1Nf(k) of the sequence {f(n)} as n→∞, if the average value exists.

Publication Title

Ramanujan Journal

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