Turán inequalities for symmetric orthogonal polynomials

Abstract

A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions.

Keywords

• recurrence relations
• Turán determinants
• Pollaczek polynomials
• Lommel polynomials
• q-Bessel functions.