{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T11:10:08Z","timestamp":1746097808895,"version":"3.40.4"},"reference-count":6,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Excellent Young Teacher Foundation of Shanghai","award":["sxy10004","A-0201-00-050-205"],"award-info":[{"award-number":["sxy10004","A-0201-00-050-205"]}]},{"name":"Foundation of Shanghai Business School","award":["sxy10004","A-0201-00-050-205"],"award-info":[{"award-number":["sxy10004","A-0201-00-050-205"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev polynomials of the second kind. Furthermore, we also obtain the complex factorizations of the second Lucas sequence by the similar matrix method using Chebyshev polynomials of the first kind.<\/jats:p>","DOI":"10.1155\/2014\/387675","type":"journal-article","created":{"date-parts":[[2014,1,2]],"date-time":"2014-01-02T21:03:48Z","timestamp":1388696628000},"page":"1-6","source":"Crossref","is-referenced-by-count":4,"title":["Complex Factorizations of the Lucas Sequences via Matrix Methods"],"prefix":"10.1155","volume":"2014","author":[{"given":"Honglin","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Business School, Shanghai 201400, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"2000","series-title":"Popular Lectures on Number Theory","key":"1"},{"issue":"1","key":"2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/00150517.2003.12428599","volume":"41","year":"2003","journal-title":"The Fibonacci Quarterly"},{"issue":"3","key":"3","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1080\/00150517.2004.12428416","volume":"42","year":"2004","journal-title":"The Fibonacci Quarterly"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.03.001"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.12.025"},{"year":"2003","key":"6"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/387675.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/387675.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/387675.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T10:38:30Z","timestamp":1746095910000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/387675\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":6,"alternative-id":["387675","387675"],"URL":"https:\/\/doi.org\/10.1155\/2014\/387675","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}