Log-concavity of the Chen–Gu ratio sequence of Boros–Moll coefficients

Abstract

In this preprint, we prove Chen and Gu’s 2008 conjecture on log-concavity of the ratio sequence of Boros–Moll coefficients, with strict inequality at every interior index. A positive integral interpolation and explicit fourth-derivative bounds establish the result for m ≥ 200. The remaining 18,915 inequalities for 6 ≤ m ≤ 199 are verified in exact integer arithmetic. The submission includes the manuscript and the accompanying Python verification code.