{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T15:42:55Z","timestamp":1778600575762,"version":"3.51.4"},"reference-count":0,"publisher":"National Library of Serbia","issue":"2","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Appl Anal Discrete Math","APPL ANAL DISC MATH","APPL ANAL DISCR MATH","APPL ANAL DISCRETE M"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>A formula for the finite sum of powers of cosines with fractional multiples\n   of ?\/2, viz. S(n,m) = ?m, k=1 (-1)k cos2n (k? \/ (2m + 2)),  where m and n are\n   arbitrary positive integers, is derived. In the process new and interesting\n   mathematical results are uncovered, particularly with regard to the\n   Bernoulli and Euler polynomials, while other related series are discussed.\n   It is found that the series always yields rational values, which can only be\n   evaluated by using the integer arithmetic routines in a mathematical\n   software package such as Mathematica.<\/jats:p>","DOI":"10.2298\/aadm130822018d","type":"journal-article","created":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T08:03:38Z","timestamp":1377158618000},"page":"354-377","source":"Crossref","is-referenced-by-count":10,"title":["On a finite sum with powers of cosines"],"prefix":"10.2298","volume":"7","author":[{"suffix":"C.M.","given":"Fonseca","family":"da","sequence":"first","affiliation":[{"name":"Universidade de Coimbra, Departamento de Matematica, Coimbra, Portugal"}]},{"given":"Victor","family":"Kowalenko","sequence":"additional","affiliation":[{"name":"The University of Melbourne, Department of Mathematics and Statistics, ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Victoria, Australia"}]}],"member":"1078","container-title":["Applicable Analysis and Discrete Mathematics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T12:16:31Z","timestamp":1685103391000},"score":1,"resource":{"primary":{"URL":"https:\/\/doiserbia.nb.rs\/Article.aspx?ID=1452-86301300018D"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013]]}},"URL":"https:\/\/doi.org\/10.2298\/aadm130822018d","relation":{},"ISSN":["1452-8630","2406-100X"],"issn-type":[{"value":"1452-8630","type":"print"},{"value":"2406-100X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}