{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T12:35:59Z","timestamp":1782822959066,"version":"3.54.5"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:00:00Z","timestamp":1737504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Numerous researchers have extensively studied various subfamilies of the bi-univalent function family utilizing special functions. In this paper, we introduce and investigate a new subfamily of bi-univalent functions, which is defined on the symmetric domain. This subfamily is connected to the Jacobi polynomial through the imaginary error function. We derive the initial coefficients of the Maclaurin series for functions in this subfamily, and analyze the Fekete\u2013Szeg\u0151 inequality for these functions. Additionally, by specializing the parameters in our main results, we deduce several new and significant findings.<\/jats:p>","DOI":"10.3390\/sym17020157","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T03:40:17Z","timestamp":1737517217000},"page":"157","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Subfamilies of Bi-Univalent Functions Associated with the Imaginary Error Function and Subordinate to Jacobi Polynomials"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9287-7704","authenticated-orcid":false,"given":"Ala","family":"Amourah","sequence":"first","affiliation":[{"name":"Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman"},{"name":"Applied Science Research Center, Applied Science Private University, Amman 11937, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8608-8063","authenticated-orcid":false,"given":"Basem","family":"Frasin","sequence":"additional","affiliation":[{"name":"Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0211-3677","authenticated-orcid":false,"given":"Jamal","family":"Salah","sequence":"additional","affiliation":[{"name":"College of Applied and Health Sciences, A\u2019Sharqiyah University, P.O. Box 42, Ibra 400, Oman"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2740-7081","authenticated-orcid":false,"given":"Feras","family":"Yousef","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Jordan, Amman 11942, Jordan"},{"name":"Department of Mathematics, Hampton University, Hampton, VA 23669, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"ref_1","first-page":"411","article-title":"Recherches sur Laattraction des Sph\u00e9roides Homog\u00e9nes","volume":"Volume 10","author":"Legendre","year":"1785","journal-title":"M\u00e9moires de l\u2019Acad\u00e9mie Royale de Sciences"},{"key":"ref_2","first-page":"228","article-title":"Collection of bi-univalent functions using bell distribution associated with Jacobi polynomials","volume":"25","author":"Amourah","year":"2025","journal-title":"Int. J. 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