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

  Published:2011-02-10
 Printed: Jun 2011
  • William Y. C. Chen,
    Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. China
  • Larry X. W. Wang,
    Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. China
  • Arthur L. B. Yang,
    Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. China
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Abstract

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 log-concavity, $q$-log-convexity, strong $q$-log-convexity, Bell polynomials, Bessel polynomials, Ramanujan polynomials, Dowling polynomials
MSC Classifications: 05A20, 05E99 show english descriptions Combinatorial inequalities
None of the above, but in this section
05A20 - Combinatorial inequalities
05E99 - None of the above, but in this section
 

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