{"id":"https://openalex.org/W7204944986","doi":"https://doi.org/10.48550/arxiv.2608.30304","title":"The Erd\u00e9lyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials","display_name":"The Erd\u00e9lyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204944986","doi":"https://doi.org/10.48550/arxiv.2608.30304"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30304","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30304","pdf_url":"https://arxiv.org/pdf/2608.30304","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031115758","display_name":"Qifeng Bai","orcid":"https://orcid.org/0000-0001-7296-6187","observed_orcids":["https://orcid.org/0000-0001-7296-6187"]},"institutions":[{"id":"https://openalex.org/I4400600959","display_name":"Nanfang College Guangzhou","ror":"https://ror.org/04vrxqg89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4400600959"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai, Qi-Feng","raw_affiliation_strings":["School of Mathematics and Statistics , Nanfang College , Guangzhou , 510970 , Guangdong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Nanfang College , Guangzhou , 510970 , Guangdong , China","institution_ids":["https://openalex.org/I4400600959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083110598","display_name":"Yu-Tian Li","orcid":"https://orcid.org/0000-0001-5638-6406","observed_orcids":["https://orcid.org/0000-0001-5638-6406"]},"institutions":[{"id":"https://openalex.org/I4400600959","display_name":"Nanfang College Guangzhou","ror":"https://ror.org/04vrxqg89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4400600959"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Yu-Tian","raw_affiliation_strings":["School of Mathematics and Statistics , Nanfang College , Guangzhou , 510970 , Guangdong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Nanfang College , Guangzhou , 510970 , Guangdong , China","institution_ids":["https://openalex.org/I4400600959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4400600959"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9990000128746033,"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":0.9990000128746033,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":9.999999747378752e-05,"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/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.9229999780654907},{"id":"https://openalex.org/keywords/christoffel-function","display_name":"Christoffel function","score":0.7179999947547913},{"id":"https://openalex.org/keywords/extremal-polynomials","display_name":"extremal polynomials","score":0.5490000247955322},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"orthogonal polynomials","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8593999743461609},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.6586999893188477},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.46959999203681946},{"id":"https://openalex.org/C77850982","wikidata":"https://www.wikidata.org/wiki/Q847816","display_name":"Christoffel symbols","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.4074999988079071},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40220001339912415},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32089999318122864},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.30070000886917114},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.2978000044822693},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C2780639617","wikidata":"https://www.wikidata.org/wiki/Q6516972","display_name":"Quadrant (abdomen)","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27649998664855957},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2554999887943268},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2554999887943268},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C118431652","wikidata":"https://www.wikidata.org/wiki/Q17098827","display_name":"Mehler\u2013Heine formula","level":5,"score":0.2524999976158142},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30304","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30304","pdf_url":"https://arxiv.org/pdf/2608.30304","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.30304","doi":"https://doi.org/10.48550/arxiv.2608.30304","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30304","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30304","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30304","pdf_url":"https://arxiv.org/pdf/2608.30304","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204944986.pdf","grobid_xml":"https://content.openalex.org/works/W7204944986.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1971659422","https://openalex.org/W2034843144","https://openalex.org/W2061434054"],"related_works":["https://openalex.org/W2034843144","https://openalex.org/W2949115401","https://openalex.org/W2061434054","https://openalex.org/W2029388807","https://openalex.org/W7098149566","https://openalex.org/W1971659422","https://openalex.org/W2000986260","https://openalex.org/W2140039029","https://openalex.org/W861749648","https://openalex.org/W1980626214"],"abstract_inverted_index":{"Let":[0],"$p_n^{(\u03b1,\u03b2)}$":[1],"denote":[2],"the":[3,8,20,37,46,56,63,79,89,94],"Jacobi":[4,107],"polynomial":[5],"orthonormal":[6],"for":[7,106],"weight":[9],"$(1-x)^\u03b1(1+x)^\u03b2$":[10],"on":[11],"$[-1,1]$,":[12],"where":[13],"$\u03b1,\u03b2\\ge-1/2$,":[14],"and":[15,44,59,110],"put":[16],"$S=\u03b1+\u03b2+1$.":[17],"We":[18,100],"prove":[19],"uniform":[21],"degree--parameter":[22],"estimate":[23,54,96],"$$":[24,29],"(1-x)^{\u03b1+1/2}(1+x)^{\u03b2+1/2}":[25],"\\bigl|p_n^{(\u03b1,\u03b2)}(x)\\bigr|^2":[26],"\\le":[27],"C\\max\\bigl\\{1,S^{1/3},S^{1/2}(n+1)^{-1/6}\\bigr\\}.":[28],"This":[30],"proves,":[31],"in":[32,55,93],"an":[33],"equivalent":[34],"symmetric":[35],"parametrisation,":[36],"stronger":[38],"degree-sensitive":[39,103],"conjecture":[40],"proposed":[41],"by":[42],"Krasikov":[43],"implies":[45],"Erd\u00e9lyi--Magnus--Nevai":[47],"conjecture.":[48],"The":[49],"proof":[50],"starts":[51],"from":[52],"Krasikov's":[53],"high-parameter":[57],"quadrant":[58],"transports":[60],"it":[61],"to":[62],"hard":[64],"edges":[65],"through":[66],"weighted":[67],"contiguous":[68],"relations":[69],"whose":[70],"singular":[71],"endpoint":[72,81],"terms":[73],"cancel;":[74],"direct":[75],"hypergeometric":[76],"estimates":[77],"control":[78],"remaining":[80],"caps.":[82],"A":[83],"Bessel":[84],"turning-point":[85],"argument":[86],"shows":[87],"that":[88],"intermediate":[90],"factor":[91],"$S^{1/3}$":[92],"squared":[95],"cannot":[97],"be":[98],"omitted.":[99],"also":[101],"derive":[102],"lower":[104],"bounds":[105],"Christoffel":[108],"functions":[109],"Gauss--Jacobi":[111],"quadrature":[112],"weights.":[113]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
