{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T03:01:41Z","timestamp":1648695701826},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p> This paper is devoted to exploring asymptotic behavior of the Sz\u00e1sz\u2013Mirakian-type operators including the Sz\u00e1sz\u2013Mirakian operators S<jats:sub>n<\/jats:sub>(f;x) and its two kinds of integral modifications [Formula: see text], [Formula: see text]. For these operators, we obtain the complete asymptotic expansions in the form of [Formula: see text] all coefficients a<jats:sub>k<\/jats:sub> (f;x) of n<jats:sup>-k<\/jats:sup> (k=1,2,\u2026) are calculated explicitly in terms of the Stirling numbers of the first and second kind. <\/jats:p>","DOI":"10.1142\/s021969130900329x","type":"journal-article","created":{"date-parts":[[2009,12,8]],"date-time":"2009-12-08T04:36:16Z","timestamp":1260246976000},"page":"851-858","source":"Crossref","is-referenced-by-count":0,"title":["THE COMPLETE ASYMPTOTIC EXPANSIONS FOR THE SZ\u00c1SZ\u2013MIRAKIAN-TYPE OPERATORS"],"prefix":"10.1142","volume":"07","author":[{"given":"CHUNGOU","family":"ZHANG","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"QUAN-E","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","first-page":"201","volume":"150","author":"Mirakian G.","journal-title":"Dokl. Akad. NauksssR"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(02)00661-1"},{"key":"rf3","volume-title":"Combinatorics","author":"Sha J.","year":"1993"},{"key":"rf4","volume-title":"Combinatorial Theory","author":"Zhao K.","year":"1981"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5295"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-004-3632-y"},{"key":"rf7","first-page":"428","volume":"32","author":"Sikkema P. C.","journal-title":"Indag. Math."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021969130900329X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:17:00Z","timestamp":1565147820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021969130900329X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":7,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.1142\/S021969130900329X"],"URL":"https:\/\/doi.org\/10.1142\/s021969130900329x","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}