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arXiv · 1308.2961

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

Donna Q. J. Dou·Anne X. Y. Ren
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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 $π$. 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.

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Donna Q. J. Dou, Anne X. Y. Ren. 2013-08-13. The $q$-log-convexity of Domb's polynomials. https://arxiv.org/abs/1308.2961

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