Abstract
We prove the convexity of the largest zero of the q-Lommel, the associated AL-Salam Carlitz II and the q-associated Laguerre polynomials as well as the convexity of products of certain functions with the largest zero of the q-associated Laguerre polynomials and associated Al-Salam–Carlitz II polynomials. Moreover, as a consequence of our results concerning the q-associated Laguerre polynomials, we find a recent result regarding the convexity of the function (1/(α + 1))x n , 1(α), where x n , 1(α) is the largest zero of the classical Laguerre
Acknowledgements
Eugenia N. Petropoulou was supported by a Postdoc Grant from the National Foundation of Scholarships (I.K.Y.). Ioannis D. Stabolas was partially supported by the National Foundation of Scholarships (I.K.Y.).