Certain products of sums of Lambert series
Aung Phone Maw
TL;DR
This paper proves an identity transforming a sum of Lambert series into an infinite product form and derives additional identities involving products of Lambert series, using elementary methods.
Contribution
It provides a new elementary proof of a Lambert series identity and introduces two novel identities for products of Lambert series.
Findings
Established an infinite product form for a Lambert series sum
Derived two new identities for products of Lambert series
Simplified proofs using elementary techniques
Abstract
Using elementary means, we prove an identity giving the infinite product form of a sum of Lambert series originally stated by Venkatachaliengar, then rediscovered by Andrews, Lewis, and Liu. Then we derive two identities expressing certain products of sums of Lambert series.
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Taxonomy
TopicsExperimental and Theoretical Physics Studies · Sports Dynamics and Biomechanics