Year: 2026
Type: article
Abstract: The classical Lambert series is given by $$ L(x)= \sum _{\nu =1}^\infty \frac{x^{\nu }}{1-x^{\nu }}, \quad |x|<1. $$ L ( x ) = ∑ ν = 1 ∞ x ν 1 - x ν , | x | < 1 . We prove that the function $$t\mapsto L(1-e^{-t})$$ t ↦ L ( 1 - e - t ) is strictly convex and strictly log-concave on $$[0,\infty )$$ [ 0 , ∞ ) . Moreover, we use these results to deduce some functional inequalities for the Lambert series.
Source: The Ramanujan Journal
Authors: Horst Alzer, Hans W. Volkmer
Institution: University of Wisconsin–Milwaukee
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7153277370