{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:30:42Z","timestamp":1760232642474,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,20]],"date-time":"2022-11-20T00:00:00Z","timestamp":1668902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research (DSR)","award":["G: 716-130-1443"],"award-info":[{"award-number":["G: 716-130-1443"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Inequalities play a fundamental role in both theoretical and applied mathematics and contain many patterns of symmetries. In many studies, inequalities have been used to provide estimates of some functions based on the properties of their symmetry. In this paper, we present the following new asymptotic expansion related to the ordinary gamma function \u0393(1+w)\u223c2\u03c0w(w\/e)ww2+760w2\u2212120w\/2exp\u2211r=1\u221e\u03bcrwr,w\u2192\u221e, with the recurrence relation of coefficients \u03bcr. Furthermore, we use Pad\u00e9 approximants and our new asymptotic expansion to deduce the new bounds of \u0393(w) better than some of its recent ones.<\/jats:p>","DOI":"10.3390\/sym14112459","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T03:09:30Z","timestamp":1669000170000},"page":"2459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Some Asymptotic Expansions for the Gamma Function"],"prefix":"10.3390","volume":"14","author":[{"given":"Mansour","family":"Mahmoud","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanan","family":"Almuashi","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"335","DOI":"10.7153\/jmi-04-30","article-title":"Very accurate approximations for the factorial function","volume":"4","author":"Batir","year":"2010","journal-title":"J. Math. Inequal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1073\/pnas.75.1.40","article-title":"Decision procedure for indefinite hypergeometric summation","volume":"75","author":"Gosper","year":"1978","journal-title":"Proc. Natl. Acad. Sci. 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