Recurrence Relations for Strongly $q$-Log-Convex Polynomials

Canadian mathematical bulletin

Arthur L. B. Yang¹  Larry X. W. Wang¹  William Y. C. Chen¹ 

[1] Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. China

关键词: log-concavity;    $q$-log-convexity;    strong $q$-log-convexity;    Bell polynomials;    Bessel polynomials;    Ramanujan polynomials;    Dowling polynomials;   

DOI  :  10.4153/CMB-2011-008-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We consider a class ofstrongly $q$-log-convex polynomials based on a triangular recurrencerelation with linear coefficients, and we show that the Bellpolynomials, the Bessel polynomials, the Ramanujan polynomials andthe Dowling polynomials are strongly $q$-log-convex. We also provethat the Bessel transformation preserves log-convexity.

【 授权许可】

Unknown