{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:10:00Z","timestamp":1760058600698,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T00:00:00Z","timestamp":1744588800000},"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>In this paper, we present some new symmetric bounds for the gamma and polygamma functions. For this goal, we present two functions involving gamma and polygamma functions and we investigate their complete monotonicity. Also, we investigate their completely monotonic degrees. This concept gives more accuracy in measuring the complete monotonicity property. These new bounds are better than some of the recently published results.<\/jats:p>","DOI":"10.3390\/sym17040595","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T09:06:51Z","timestamp":1744621611000},"page":"595","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some New Inequalities for the Gamma and Polygamma Functions"],"prefix":"10.3390","volume":"17","author":[{"given":"Waad","family":"Al Sayed","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Sciences and Humanities, Fahad Bin Sultan University, P.O. Box 15700, Tabuk 71454, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2792-6239","authenticated-orcid":false,"given":"Hesham","family":"Moustafa","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Sciences and Humanities, Fahad Bin Sultan University, P.O. Box 15700, Tabuk 71454, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,14]]},"reference":[{"key":"ref_1","unstructured":"Sandor, J. (2005). Selected Chapters of Gometry, Analysis and Number Theory. RGMIA Monographs, Victoria University."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Abramowitz, M., and Stegun, I.A. (1965). Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables.","DOI":"10.1063\/1.3047921"},{"key":"ref_3","first-page":"917","article-title":"Sharp bounds for the psi function and harmonic numbers","volume":"14","author":"Batir","year":"2011","journal-title":"Math. Inequal. Appl."},{"key":"ref_4","unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). 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