{"id":"https://openalex.org/W2008597311","doi":"https://doi.org/10.1137/060651896","title":"Ultraspherical Stieltjes Polynomials and Gauss\u2013Kronrod Quadrature Behave Nicely for $\\lambda&lt; 0$","display_name":"Ultraspherical Stieltjes Polynomials and Gauss\u2013Kronrod Quadrature Behave Nicely for $\\lambda&lt; 0$","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2008597311","doi":"https://doi.org/10.1137/060651896","mag":"2008597311"},"language":"en","primary_location":{"id":"doi:10.1137/060651896","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060651896","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019567446","display_name":"B. de la Calle Ysern","orcid":"https://orcid.org/0000-0003-2842-2611"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"B. de la Calle Ysern","raw_affiliation_strings":["Technical University Of Madrid"],"affiliations":[{"raw_affiliation_string":"Technical University Of Madrid","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042081362","display_name":"Franz Peherstorfer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Peherstorfer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019567446"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":null,"apc_paid":null,"fwci":1.7941,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81729686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":"2","first_page":"770","last_page":"786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8193091750144958},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.7970541715621948},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.6490126848220825},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6074612140655518},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.5703876614570618},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.552475094795227},{"id":"https://openalex.org/keywords/riemann\u2013stieltjes-integral","display_name":"Riemann\u2013Stieltjes integral","score":0.5347871780395508},{"id":"https://openalex.org/keywords/mehler\u2013heine-formula","display_name":"Mehler\u2013Heine formula","score":0.46526458859443665},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4482845067977905},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.39734312891960144},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34739094972610474},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.12897443771362305},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.055246204137802124}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8193091750144958},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.7970541715621948},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6490126848220825},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6074612140655518},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.5703876614570618},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.552475094795227},{"id":"https://openalex.org/C167211080","wikidata":"https://www.wikidata.org/wiki/Q285771","display_name":"Riemann\u2013Stieltjes integral","level":3,"score":0.5347871780395508},{"id":"https://openalex.org/C118431652","wikidata":"https://www.wikidata.org/wiki/Q17098827","display_name":"Mehler\u2013Heine formula","level":5,"score":0.46526458859443665},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4482845067977905},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.39734312891960144},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34739094972610474},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.12897443771362305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.055246204137802124},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060651896","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060651896","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W188408891","https://openalex.org/W604181985","https://openalex.org/W650542949","https://openalex.org/W1581686711","https://openalex.org/W1650035168","https://openalex.org/W1964501944","https://openalex.org/W1965838664","https://openalex.org/W1969598910","https://openalex.org/W1974860839","https://openalex.org/W1999348006","https://openalex.org/W2011624878","https://openalex.org/W2014099887","https://openalex.org/W2019254344","https://openalex.org/W2022937469","https://openalex.org/W2023900389","https://openalex.org/W2023978509","https://openalex.org/W2027623824","https://openalex.org/W2033735550","https://openalex.org/W2048041816","https://openalex.org/W2050191834","https://openalex.org/W2066956883","https://openalex.org/W2155263269"],"related_works":["https://openalex.org/W2793709684","https://openalex.org/W2045154321","https://openalex.org/W2489863694","https://openalex.org/W1896660781","https://openalex.org/W4298399453","https://openalex.org/W4287597771","https://openalex.org/W3105011789","https://openalex.org/W2005041925","https://openalex.org/W2504939013","https://openalex.org/W1651872008"],"abstract_inverted_index":{"We":[0,31,60],"show":[1],"that":[2,34,62],"the":[3,6,11,39,42,55,63,82],"zeros":[4,40],"of":[5,26,41,65,75],"Stieltjes":[7,76],"polynomials":[8,77],"associated":[9],"with":[10,15,38,51],"ultraspherical":[12,44],"weight":[13],"function":[14],"parameter":[16],"$\\lambda<0$":[17],"are":[18,69],"real":[19],"and":[20],"simple":[21],"and,":[22],"except":[23],"for":[24],"two":[25,52],"them,":[27],"belong":[28],"to":[29],"$(-1,1)$.":[30],"also":[32],"prove":[33,61],"they":[35],"strictly":[36],"interlace":[37],"corresponding":[43],"polynomials.":[45],"Consequently,":[46],"a":[47],"Gauss\u2013Kronrod":[48],"quadrature":[49,67],"formula":[50],"nodes":[53],"outside":[54],"interval":[56,84],"$[-1,1]$":[57,85],"is":[58,86],"obtained.":[59],"coefficients":[64],"such":[66],"rules":[68],"positive.":[70],"Finally,":[71],"an":[72],"asymptotic":[73],"representation":[74],"which":[78],"converges":[79],"uniformly":[80],"on":[81],"whole":[83],"provided.":[87]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}