{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T20:14:43Z","timestamp":1775765683310,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T00:00:00Z","timestamp":1667433600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["780"],"award-info":[{"award-number":["780"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The function PL(z)=1+z maps the unit disc D={z\u2208C:|z|&lt;1} to a leminscate which is symmetric about the x-axis. The conditions on the parameters \u03b1 and n, for which the associated Laguerre polynomial (ALP) Ln\u03b1 maps unit disc into the leminscate domain, are deduced in this article. We also establish the condition under which a function involving Ln\u03b1 maps D to a domain subordinated by \u03d5Ne(z)=1\u2212z+z3\/3, \u03d5e(z)=ez, and \u03d5A(z)=1+Az, A\u2208(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.<\/jats:p>","DOI":"10.3390\/sym14112303","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T04:11:31Z","timestamp":1667448691000},"page":"2303","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mapping Properties of Associate Laguerre Polynomials in Leminiscate, Exponential and Nephroid Domain"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4540-1601","authenticated-orcid":false,"given":"Saiful R.","family":"Mondal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,3]]},"reference":[{"key":"ref_1","unstructured":"Abramowitz, M., and Stegun, I.A. 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