Recurrence Relations for Strongly q-Log-Convex Polynomials

TL;DR

This paper investigates a class of strongly q-log-convex polynomials defined by recurrence relations, demonstrating their properties in well-known polynomial families and showing that Bessel transformation preserves log-convexity.

Contribution

It introduces a new class of strongly q-log-convex polynomials based on recurrence relations and proves their properties for several classical polynomial families.

Findings

Bell polynomials are strongly q-log-convex

Bessel polynomials are strongly q-log-convex

Bessel transformation preserves log-convexity

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.