{"id":"https://openalex.org/W7203735822","doi":"https://doi.org/10.48550/arxiv.2608.17221","title":"Romanovski polynomials, Gegenbauer connections, and $\\mathrm{su}(1,1)$ ladder structures","display_name":"Romanovski polynomials, Gegenbauer connections, and $\\mathrm{su}(1,1)$ ladder structures","publication_year":2026,"publication_date":"2026-08-18","ids":{"openalex":"https://openalex.org/W7203735822","doi":"https://doi.org/10.48550/arxiv.2608.17221"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.17221","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17221","pdf_url":"https://arxiv.org/pdf/2608.17221","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/2608.17221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106193501","display_name":"Jos\u00e9 A. Vallejo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I178450904","display_name":"Universidad Nacional de Educaci\u00f3n a Distancia","ror":"https://ror.org/02msb5n36","country_code":"ES","type":"education","lineage":["https://openalex.org/I178450904"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Vallejo, Jos\u00e9 A.","raw_affiliation_strings":["Departamento de Matem\u00e1ticas Fundamentales , Universidad Nacional de Educaci\u00f3n a Distancia , Madrid , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas Fundamentales , Universidad Nacional de Educaci\u00f3n a Distancia , Madrid , Spain","institution_ids":["https://openalex.org/I178450904"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089878743","display_name":"M. Kirchbach","orcid":"https://orcid.org/0000-0002-4264-3296","observed_orcids":["https://orcid.org/0000-0002-4264-3296"]},"institutions":[{"id":"https://openalex.org/I196664497","display_name":"Autonomous University of San Luis Potos\u00ed","ror":"https://ror.org/000917t60","country_code":"MX","type":"education","lineage":["https://openalex.org/I196664497"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Kirchbach, Mariana","raw_affiliation_strings":["Instituto de F\u00edsica , Universidad Aut\u00f3noma de San Luis Potos\u00ed , San Luis Potos\u00ed , Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de F\u00edsica , Universidad Aut\u00f3noma de San Luis Potos\u00ed , San Luis Potos\u00ed , Mexico","institution_ids":["https://openalex.org/I196664497"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.9909999966621399},{"id":"https://openalex.org/keywords/connection-problem","display_name":"connection problem","score":0.6579999923706055},{"id":"https://openalex.org/keywords/creation-and-annihilation-operators","display_name":"creation and annihilation operators","score":0.6579999923706055},{"id":"https://openalex.org/keywords/three-term-recurrence-relation","display_name":"three-term recurrence relation","score":0.9110000133514404},{"id":"https://openalex.org/keywords/monic-polynomials","display_name":"monic polynomials","score":0.49799999594688416},{"id":"https://openalex.org/keywords/trigonometric-substitution","display_name":"trigonometric substitution","score":0.6710000038146973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8019000291824341},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.6575000286102295},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.489300012588501},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.47909998893737793},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.412200003862381},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.40709999203681946},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.37599998712539673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36980000138282776},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.35429999232292175},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.35179999470710754},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30469998717308044},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.17221","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17221","pdf_url":"https://arxiv.org/pdf/2608.17221","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.2608.17221","doi":"https://doi.org/10.48550/arxiv.2608.17221","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.17221","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:2608.17221","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17221","pdf_url":"https://arxiv.org/pdf/2608.17221","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/W7203735822.pdf","grobid_xml":"https://content.openalex.org/works/W7203735822.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2042071920","https://openalex.org/W2114298976","https://openalex.org/W2162821008","https://openalex.org/W2113014066","https://openalex.org/W4322625460","https://openalex.org/W7134808817","https://openalex.org/W7100148147","https://openalex.org/W7120364357","https://openalex.org/W7223159419","https://openalex.org/W2029219807"],"abstract_inverted_index":{"We":[0,14,44],"study":[1],"the":[2,17,33,41,49,53,58,63,67,72,105,123,127],"monic":[3],"Romanovski":[4,116],"(pseudo-Jacobi)":[5],"polynomials":[6,117],"with":[7,27,52,57,118],"degree":[8],"dependent":[9],"parameters":[10],"$\u03b2_K=-K$":[11],"and":[12,61,98,130,145],"$\u03b1_K=c/(K+1)$.":[13],"write":[15],"out":[16],"parameter":[18,120],"preserving":[19],"first":[20],"order":[21,110],"ladder":[22,64],"relations":[23,65,114],"at":[24],"fixed":[25,91],"$(\u03b1,\u03b2)$,":[26],"real":[28],"constants.":[29],"Combining":[30],"them":[31,37],"returns":[32],"three-term":[34],"recurrence;":[35],"iterating":[36],"builds":[38],"$R_n^{\u03b1,\u03b2}$":[39],"from":[40,138],"constant":[42],"polynomial.":[43],"solve":[45],"in":[46,126],"triangular":[47],"form":[48],"connection":[50],"problem":[51],"$\u03b1=0$":[54],"family,":[55],"identified":[56],"Gegenbauer":[59],"polynomials,":[60],"transfer":[62],"to":[66],"$(n,\\ell)$":[68],"lattice.":[69],"Under":[70],"$x=\\cot\u03c7$":[71],"in-level":[73],"operators":[74],"depend":[75],"on":[76],"$\\ell$":[77],"alone.":[78],"The":[79,101],"dressed":[80],"functions":[81,103],"carry":[82,104],"intrinsic":[83],"lowest":[84],"weight":[85],"$\\mathrm{su}(1,1)$":[86],"modules":[87,107],"along":[88],"columns":[89],"of":[90],"$\\ell$;":[92],"rows":[93],"need":[94],"a":[95,99],"boundary":[96],"prescription":[97],"rescaling.":[100],"deformed":[102],"same":[106],"through":[108],"higher":[109],"operators,":[111],"which":[112,134,146],"yield":[113],"between":[115],"different":[119],"pairs.":[121],"Algebraically":[122],"family":[124],"lies":[125],"Jacobi":[128],"class,":[129],"we":[131],"indicate":[132],"throughout":[133],"statements":[135],"are":[136,147],"inherited":[137],"that":[139],"framework":[140],"by":[141],"transformation":[142],"or":[143],"specialization":[144],"not.":[148]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-20T00:00:00"}
