On a class of generalized Laguerre's polynomials
MSC 2010: 33C20
The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in...
S. K. Chatterjea has recently proved a class of generating relations involving ultraspherical polynomials from the view point of continuous transformations-groups. The object of the present paper is to point out that this class of generating relations implies the explicit representation, the addition and the multiplication formulas, in addition to the usual generating relation for the ultraspherical polynomials.