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Recurrence Relations for Strongly q-Log-Convex Polynomials

Published online by Cambridge University Press:  20 November 2018

William Y. C. Chen ,
Larry X. W. Wang  and
Arthur L. B. Yang
William Y. C. Chen
Affiliation:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. Chinae-mail: chen@nankai.edu.cnwxw@cfc.nankai.edu.cnyang@nankai.edu.cn
Larry X. W. Wang
Affiliation:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. Chinae-mail: chen@nankai.edu.cnwxw@cfc.nankai.edu.cnyang@nankai.edu.cn
Arthur L. B. Yang
Affiliation:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. Chinae-mail: chen@nankai.edu.cnwxw@cfc.nankai.edu.cnyang@nankai.edu.cn
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Abstract

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We consider a class of strongly $q$-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly $q$-log-convex. We also prove that the Bessel transformation preserves log-convexity.

Keywords

05A2005E99log-concavityq-log-convexitystrongq-log-convexityBell polynomialsBessel polynomialsRamanujan polynomialsDowling polynomials
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 217 - 229
Copyright
Copyright © Canadian Mathematical Society 2011

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