{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T22:26:23Z","timestamp":1764109583275,"version":"3.46.0"},"reference-count":0,"publisher":"University of Calgary","issue":"4","license":[{"start":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T00:00:00Z","timestamp":1736985600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Contrib Discrete Math"],"abstract":"<jats:p>We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries\u2019 natural and deep connection with Bernoulli polynomials, a special case of the matrix can be constructed from a corresponding Vandermonde matrix. As a result, instead of asymptotic analysis, we give a direct proof of calculating an entry of its inverse. Further extensions also include an identity of Stirling numbers of the both kinds.<\/jats:p>","DOI":"10.55016\/ojs\/cdm.v19i4.74294","type":"journal-article","created":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T16:47:21Z","timestamp":1762620441000},"page":"64-84","source":"Crossref","is-referenced-by-count":0,"title":["Hankel determinants of certain sequences of Bernoulli polynomials"],"prefix":"10.55016","volume":"19","author":[{"given":"Lin","family":"Jiu","sequence":"first","affiliation":[]},{"given":"Ye","family":"Li","sequence":"additional","affiliation":[]}],"member":"13844","published-online":{"date-parts":[[2025,1,16]]},"container-title":["Contributions to Discrete Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/74294\/57959","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/74294\/57959","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T22:21:40Z","timestamp":1764109300000},"score":1,"resource":{"primary":{"URL":"https:\/\/cdm.ucalgary.ca\/article\/view\/74294"}},"subtitle":["A direct proof of an inverse matrix entry from statistics"],"short-title":[],"issued":{"date-parts":[[2025,1,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,1,16]]}},"URL":"https:\/\/doi.org\/10.55016\/ojs\/cdm.v19i4.74294","relation":{},"ISSN":["1715-0868"],"issn-type":[{"type":"electronic","value":"1715-0868"}],"subject":[],"published":{"date-parts":[[2025,1,16]]}}}