{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:37:51Z","timestamp":1773149871112,"version":"3.50.1"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"268","license":[{"start":{"date-parts":[[2010,2,11]],"date-time":"2010-02-11T00:00:00Z","timestamp":1265846400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are log-concave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a conjecture which is stronger than Moll\u2019s conjecture on the \n\n \n \u221e<\/mml:mi>\n \\infty<\/mml:annotation>\n <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>-log-concavity.<\/p>","DOI":"10.1090\/s0025-5718-09-02223-6","type":"journal-article","created":{"date-parts":[[2009,6,30]],"date-time":"2009-06-30T14:39:02Z","timestamp":1246372742000},"page":"2269-2282","source":"Crossref","is-referenced-by-count":20,"title":["The ratio monotonicity of the Boros-Moll polynomials"],"prefix":"10.1090","volume":"78","author":[{"given":"William","family":"Chen","sequence":"first","affiliation":[]},{"given":"Ernest","family":"Xia","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"issue":"1","key":"1","first-page":"Research Paper 30, 7","article-title":"An extension of a criterion for unimodality","volume":"8","author":"Alvarez, Jenny","year":"2001","journal-title":"Electron. J. Combin."},{"key":"2","unstructured":"T. Amdeberhan and V. H. Moll, A formula for a quartic integral: a survey of old proofs and some new ones, Ramanujan J., to appear."},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/S0377-0427(99)00081-3","article-title":"An integral hidden in Gradshteyn and Ryzhik","volume":"106","author":"Boros, George","year":"1999","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1006\/jmaa.1999.6479","article-title":"A sequence of unimodal polynomials","volume":"237","author":"Boros, George","year":"1999","journal-title":"J. Math. Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-247X","issn-type":"print"},{"key":"5","first-page":"Research Paper 10, 4","article-title":"A criterion for unimodality","volume":"6","author":"Boros, George","year":"1999","journal-title":"Electron. J. Combin."},{"issue":"1-2","key":"6","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/S0377-0427(99)00372-6","article-title":"The double square root, Jacobi polynomials and Ramanujan\u2019s master theorem","volume":"130","author":"Boros, George","year":"2001","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"7","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511617041","volume-title":"Irresistible integrals","author":"Boros, George","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/0521796369"},{"key":"8","unstructured":"W. Y. C. Chen and E. X. W. Xia, The ratio monotonicity of the \ud835\udc5e-derangement numbers, arXiv:math.CO\/0708.2572."},{"issue":"12","key":"9","doi-asserted-by":"publisher","first-page":"3847","DOI":"10.1090\/S0002-9939-07-08912-5","article-title":"A computer proof of Moll\u2019s log-concavity conjecture","volume":"135","author":"Kauers, Manuel","year":"2007","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"issue":"3","key":"10","first-page":"311","article-title":"The evaluation of integrals: a personal story","volume":"49","author":"Moll, Victor H.","year":"2002","journal-title":"Notices Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9920","issn-type":"print"},{"issue":"2","key":"11","first-page":"Art. 4, 17","article-title":"Combinatorial sequences arising from a rational integral","author":"Moll, Victor H.","year":"2007","journal-title":"Online J. Anal. Comb."},{"key":"12","unstructured":"K. Wegschaider, Computer generated proofs of binomial multi-sum identities, Master\u2019s thesis, RISC-Linz, May 1997."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-268\/S0025-5718-09-02223-6\/S0025-5718-09-02223-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-268\/S0025-5718-09-02223-6\/S0025-5718-09-02223-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T03:41:42Z","timestamp":1627616502000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-268\/S0025-5718-09-02223-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,11]]},"references-count":12,"journal-issue":{"issue":"268","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["S0025-5718-09-02223-6"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-09-02223-6","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,11]]}}}