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

  Download:   pdf