Abstract
The function P-L(z) = root 1+z maps the unit disc D = {z is an element of C:vertical bar z vertical bar < 1} to a leminscate which is symmetric about the x-axis. The conditions on the parameters alpha and n, for which the associated Laguerre polynomial (ALP) L-n(alpha) maps unit disc into the leminscate domain, are deduced in this article. We also establish the condition under which a function involving L-n(alpha) maps D to a domain subordinated by phi N-e (z) = 1-z + z(3)/3, phi(e)(z) = e(z), and phi(A)(z) = 1 + Az, A is an element of (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.