Abstract
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.
Funder
Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference17 articles.
1. Abramowitz, M., and Stegun, I.A. A Handbook of Mathematical Functions, 1965.
2. Schrödinger and Dirac equations for the hydrogen atom, and Laguerre polynomials;Mawhin;Arch. Hist. Exact Sci.,2010
3. Resolving the ambiguity in the relation between Stokes shift and Huang-Rhys parameter;de Jong;Phys. Chem. Chem. Phys.,2015
4. Solution of time domain electric field integral equation using the Laguerre polynomials;Chung;IEEE Trans. Antennas Propag.,2004
5. Szegö, G. Orthogonal Polynomials, 1939. Volume 23.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献