Recurrence Relations for Strongly q-Log-Convex Polynomials

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.

15 pages

References in corpus (1)

• A note on log-convexity of q-Catalan numbers

Cited by in corpus (9)

• Total positivity of some polynomial matrices that enumerate labeled trees and forests, I. Forests of rooted labeled trees
• The Graham--Knuth--Patashnik recurrence: Symmetries and continued fractions
• On the $q$-log-convexity conjecture of Sun
• The $q$-log-convexity of Domb's polynomials
• Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials
• Total positivity from the exponential Riordan arrays
• Stieltjes moment properties and continued fractions from combinatorial triangles
• The q-Log-convexity of the Generating Functions of the Squares of Binomial Coefficients
• Positivity of iterated sequences of polynomials