Certain characterization properties of the Laguerre polynomials

Generalized Laguerre polynomials have extensively been studied in various branches of applied mathematics and theoretical physics. It has however remained unexplored in the realms of Geometric Function Theory. Our aim in the present paper is to study and investigate the basic characteristics of the normalized form of this class of polynomials. Among the results that we investigate are the results giving the characteristic properties of univalence, convexity, starlikeness, and close-to-convexity for the normalized Laguerre polynomials. We further investigate the conditions under which this normalized class of polynomials is strongly convex and strongly starlike. Several corollaries and special cases are also mentioned depicting the usefulness of the main results. The concluding section describes briefly the applications of the results presented in this paper.