Recurrence Relations for Strongly q-Log-Convex Polynomials

William Y.C. Chen, Larry X.W. Wang and Arthur L.B. Yang

  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.

  AMS Classification:  05A20, 05E99

  Keywords:  log-concave, q-log-convexity, strong q-log-convexity, Bell polynomials, Bessel polynomials, Ramanujan polynomials, Dowling polynomials

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