A unified treatment for the asymptotic normality of the coefficients of polynomials related to orthogonal ones

Suitable transformations on the orthogonal polynomials lead to polynomials with nonnegative coefficients. In this work, the asymptotic normality for the nonnegative coefficients of these polynomials is derived based on the nature of the weight function of the orthogonal polynomials. In particular, orthogonal polynomial cases from both classical and semi-classical systems are included as well as the singular behaved Pollaczek polynomial case.