{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:26Z","timestamp":1777447886963,"version":"3.51.4"},"reference-count":12,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2018,2,5]],"date-time":"2018-02-05T00:00:00Z","timestamp":1517788800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,2,5]]},"abstract":"<jats:p>In 1974, Askey and Steinig showed that for [Formula: see text] and [Formula: see text], [Formula: see text] We prove that [Formula: see text] and that the alternating sums [Formula: see text] satisfy [Formula: see text] Both inequalities hold for all [Formula: see text] and [Formula: see text]. The constant lower bounds given in ( 0.1 ) and ( 0.2 ) are best possible. The asymptotic behaviour of both sums is also investigated.<\/jats:p>","DOI":"10.3233\/asy-171447","type":"journal-article","created":{"date-parts":[[2018,2,6]],"date-time":"2018-02-06T12:58:23Z","timestamp":1517921903000},"page":"233-249","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["On a trigonometric inequality of\u00a0Askey\u00a0and\u00a0Steinig"],"prefix":"10.1177","volume":"106","author":[{"given":"Horst","family":"Alzer","sequence":"first","affiliation":[{"name":"Morsbacher Stra\u00dfe 10, 51545 Waldbr\u00f6l, Germany. E-mail:\u00a0"}]},{"given":"Man Kam","family":"Kwong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Hong Kong Polytechnic University, Hunghom, Hong Kong. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2018,2,5]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970470"},{"key":"ref002","doi-asserted-by":"crossref","unstructured":"R.\u00a0Askey and G.\u00a0Gasper, Inequalities for polynomials, in: The Bieberbach Conjecture, A.\u00a0BaernsteinII et al., eds, Math. Suveys and Monographs, Vol.\u00a02, Amer. Math. Soc., Providence, RI, 1986, pp.\u00a07\u201332.","DOI":"10.1090\/surv\/021\/02"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1974-0338481-3"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01463875"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S030500410007167X"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442671"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-001-0004-x"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-49655-4"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-3498-6_24"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2014.08.005"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1142\/1284"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-96044-4"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-171447","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-171447","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-171447","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:09Z","timestamp":1777379769000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-171447"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,5]]},"references-count":12,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2018,2,5]]}},"alternative-id":["10.3233\/ASY-171447"],"URL":"https:\/\/doi.org\/10.3233\/asy-171447","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,5]]}}}