{"data":{"id":"10.4231/r7v985z5","type":"dois","attributes":{"doi":"10.4231/r7v985z5","prefix":"10.4231","suffix":"r7v985z5","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Gautschi, Walter","givenName":"Walter","familyName":"Gautschi","affiliation":["Purdue University"],"nameIdentifiers":[{"schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0000-0001-9184-8899","nameIdentifierScheme":"ORCID"}]}],"titles":[{"title":"BIJ: Matlab programs for testing and extending Bernstein's Inequality for Jacobi polynomials"}],"publisher":"Purdue University Research Repository","container":{},"publicationYear":2014,"subjects":[{"subject":"Computer Science"},{"subject":"Bernstein’s inequality"},{"subject":"Jacobi polynomials"},{"subject":"Erdelyi–Magnus–Nevai conjecture"},{"subject":"Sharpness"},{"subject":"Orthogonal polynomials"},{"subject":"Matlab"},{"subject":"Software source code"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Walter Gautschi Archives"}],"contributors":[],"dates":[{"date":"2014-04-22","dateType":"Available"},{"date":"2014-04-22","dateType":"Submitted"},{"date":"2014-04-23","dateType":"Accepted"},{"date":"2014","dateType":"Issued"}],"language":"en","types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Datasets","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"http://eudml.org/doc/225564","resourceTypeGeneral":"JournalArticle","relatedIdentifierType":"URL"}],"relatedItems":[],"sizes":["4 files","2 KB"],"formats":["text/plain"],"version":"1.0","rightsList":[{"rights":"Creative Commons Zero v1.0 Universal","rightsUri":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc0-1.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"\u0026lt;p\u0026gt;Bernstein\u0026amp;rsquo;s inequality for Jacobi polynomials with parameters alpha, beta is analyzed here analytically and, above all, computationally with regard to validity and sharpness. Computation suggests that the inequality holds with new, somewhat larger, constants in any region R_s={-1/2\u0026amp;lt;=alpha\u0026amp;lt;=s, -1/2\u0026amp;lt;=beta\u0026amp;lt;=s}. Best constants are provided for s =1 : .5 : 4 and s =5 : 1 : 10. The work also sheds new light on the so-called Erdelyi\u0026amp;ndash;Magnus\u0026amp;ndash;Nevai conjecture for orthonormal Jacobi polynomials, adding further support for its validity and suggesting .66198126. . . as the best constant implied in the conjecture.\u0026lt;/p\u0026gt;","descriptionType":"Abstract"},{"description":"Bernstein’s inequality for Jacobi polynomials is analyzed here analytically and computationally with regard to validity and sharpness","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://purr.purdue.edu/publications/1569/1","contentUrl":null,"metadataVersion":9,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2014-04-22T15:39:34.000Z","registered":"2014-04-22T15:39:35.000Z","publi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