LAUSR

The function PL(z)=1+z maps the unit disc D={z∈C:|z|<1} to a leminscate which is symmetric about the x-axis. The conditions on the parameters α and n, for which the associated Laguerre polynomial (ALP) Lnα maps unit disc into the leminscate domain, are deduced in this article. We also establish the condition under which a function involving Lnα maps D to a domain subordinated by ϕNe(z)=1−z+z3/3, ϕe(z)=ez, and ϕA(z)=1+Az, A∈(0,1]. We provide several graphical presentations for a clear view of some of the obtained results. The possibilities for the improvements of the results are also highlighted.