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April 12, 2026The Ramanujan JournalOpen Access

Inequalities for the Lambert series

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Authors

HAHorst AlzerHVHans Volkmer

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Overview

This analytical study proves the convexity and log-concavity of the Lambert series function, indicating functional inequalities.

Key Points

  • This work aims to explore the properties of the Lambert series function relating to convexity and functional inequalities.
  • Defined the classical Lambert series and transformed it using an exponential function.
  • Proved the strict convexity of the transformed Lambert series function.
  • Established the strict log-concavity of the same function on the interval [0, ∞).
  • Derived functional inequalities from these properties.
  • Confirmed that the function is strictly convex and log-concave on the specified interval.
  • Identified several functional inequalities related to the Lambert series.

Cite This Study

Alzer et al. (2026) studied this question.

synapsesocial.com/papers/69db38274fe01fead37c64bfhttps://doi.org/10.1007/s11139-026-01365-x
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