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1. CMB 2011 (vol 54 pp. 217)
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Recurrence Relations for Strongly $q$-Log-Convex Polynomials
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:log-concavity, $q$-log-convexity, strong $q$-log-convexity, Bell polynomials, Bessel polynomials, Ramanujan polynomials, Dowling polynomials Categories:05A20, 05E99 |