The $q$-log-convexity of Domb's polynomials

TL;DR

This paper proves the $q$-log-convexity of Domb's polynomials, confirming a conjecture and establishing the log-convexity of Domb's numbers, using properties of Narayana polynomials and a specific criterion.

Contribution

It introduces a proof of the $q$-log-convexity of Domb's polynomials, a conjecture related to Ramanujan-Sato series, and derives the log-convexity of Domb's numbers.

Findings

Proved $q$-log-convexity of Domb's polynomials

Established log-convexity of Domb's numbers

Connected $q$-log-convexity with Narayana polynomials

Abstract

In this paper, we prove the $q$-log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of $\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the $q$-log-convexity of Narayana polynomials of type $B$ and a criterion for determining $q$-log-convexity of self-reciprocal polynomials.