{"id":"https://openalex.org/W2128653191","doi":"https://doi.org/10.1090/s0025-5718-08-02122-4","title":"Identifying minimal and dominant solutions for Kummer recursions","display_name":"Identifying minimal and dominant solutions for Kummer recursions","publication_year":2008,"publication_date":"2008-05-14","ids":{"openalex":"https://openalex.org/W2128653191","doi":"https://doi.org/10.1090/s0025-5718-08-02122-4","mag":"2128653191"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02122-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02122-4","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02122-4/S0025-5718-08-02122-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02122-4/S0025-5718-08-02122-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057447663","display_name":"Alfredo Dea\u00f1o","orcid":"https://orcid.org/0000-0003-1704-247X"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alfredo Dea\u00f1o","raw_affiliation_strings":["DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060535118","display_name":"Javier Segura","orcid":"https://orcid.org/0000-0002-0841-5636"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Javier Segura","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1ticas, Estad\u00c3\u00adstica y Computaci\u00c3\u00b3n, Universidad de Cantabria, 39005 Santander, Spain","Departamento de Matem\u00e1ticas, Estadistica y Computaci\u00f3n, Universidad de Cantabria, 39005 Santander, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1ticas, Estad\u00c3\u00adstica y Computaci\u00c3\u00b3n, Universidad de Cantabria, 39005 Santander, Spain","institution_ids":["https://openalex.org/I13134134"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Estadistica y Computaci\u00f3n, Universidad de Cantabria, 39005 Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034014718","display_name":"Nico \u039c. \u03a4emme","orcid":"https://orcid.org/0000-0002-8394-5223"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Nico Temme","raw_affiliation_strings":["CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5976,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.89242543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"77","issue":"264","first_page":"2277","last_page":"2293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9973999857902527,"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":0.9973999857902527,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9265536665916443},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.7998740673065186},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.5192973017692566},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5084952116012573},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.48506346344947815},{"id":"https://openalex.org/keywords/hypergeometric-distribution","display_name":"Hypergeometric distribution","score":0.4751460552215576},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.4129776954650879},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3802183270454407},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10824418067932129},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.047419190406799316},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.045321255922317505}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9265536665916443},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.7998740673065186},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.5192973017692566},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5084952116012573},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.48506346344947815},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.4751460552215576},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.4129776954650879},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3802183270454407},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10824418067932129},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.047419190406799316},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.045321255922317505}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-08-02122-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02122-4","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02122-4/S0025-5718-08-02122-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:e-archivo.uc3m.es:10016/6634","is_oa":false,"landing_page_url":"http://hdl.handle.net/10016/6634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400817","display_name":"e-Archivo (Carlos III University of Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I50357001","host_organization_name":"Universidad Carlos III de Madrid","host_organization_lineage":["https://openalex.org/I50357001"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:kar.kent.ac.uk:70232","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/70232/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02122-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02122-4","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02122-4/S0025-5718-08-02122-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2128653191.pdf","grobid_xml":"https://content.openalex.org/works/W2128653191.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1992978094","https://openalex.org/W2003051132","https://openalex.org/W2094438648","https://openalex.org/W2122684087","https://openalex.org/W2124253637","https://openalex.org/W2138075164","https://openalex.org/W2166983303","https://openalex.org/W2313299119","https://openalex.org/W2617910926","https://openalex.org/W2787895155","https://openalex.org/W2801179766","https://openalex.org/W4300223101","https://openalex.org/W6611095560","https://openalex.org/W6630467700"],"related_works":["https://openalex.org/W2756055184","https://openalex.org/W4238808391","https://openalex.org/W3103170102","https://openalex.org/W3099551705","https://openalex.org/W2028620627","https://openalex.org/W2804105606","https://openalex.org/W1530279041","https://openalex.org/W2088415640","https://openalex.org/W1502250725","https://openalex.org/W2017186500"],"abstract_inverted_index":{"We":[0],"identify":[1],"minimal":[2],"and":[3,85,246],"dominant":[4],"solutions":[5],"of":[6,220],"three-term":[7],"recurrence":[8],"relations":[9],"for":[10,206,217],"the":[11],"confluent":[12],"hypergeometric":[13],"functions":[14,208],"<inline-formula":[15,86,147,221,234,247,261],"content-type=\"math/mathml\">":[16,87,148,222,235,248,262],"<mml:math":[17,88,149,223,236,249,263],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,89,150,224,237,250,264],"alttext=\"Subscript":[19],"1":[20,24,29,96],"Baseline":[21,154],"upper":[22],"F":[23],"left-parenthesis":[25,92],"a":[26,93],"plus":[27,33,94,100],"epsilon":[28,34,95,101],"n":[30,36,97,103],"semicolon":[31,37],"c":[32,99],"2":[35,102],"z":[38,105,267],"right-parenthesis\">":[39,106],"<mml:semantics>":[40,107,160,226,239,252,271],"<mml:mrow>":[41,108,161,272],"<mml:msub>":[42,46,54,64,114,124,162],"<mml:mi/>":[43],"<mml:mn>1</mml:mn>":[44,48,58,118,174],"</mml:msub>":[45,49,59,69,119,129,167],"<mml:mi>F</mml:mi>":[47],"<mml:mo":[50,73,110,133,275,284],"stretchy=\"false\">(</mml:mo>":[51,111],"<mml:mi>a</mml:mi>":[52,112,227],"<mml:mo>+</mml:mo>":[53,63,113,123],"<mml:mi>":[55,65,115,125,163,288],"\u03f5":[56,66,116,126,164],"</mml:mi>":[57,67,117,127,165,290],"<mml:mi>n</mml:mi>":[60,70,120,130],"<mml:mo>;</mml:mo>":[61,71],"<mml:mi>c</mml:mi>":[62,122,240],"<mml:mn>2</mml:mn>":[68,128],"<mml:mi>z</mml:mi>":[72,132,253,281],"stretchy=\"false\">)</mml:mo>":[74,134],"</mml:mrow>":[75,135,175,277,286,291],"<mml:annotation":[76,136,176,228,241,254,292],"encoding=\"application/x-tex\">_1F_1(a+\\epsilon":[77],"_1":[78,138],"n;c+\\epsilon":[79],"_2":[80,140],"n;z)</mml:annotation>":[81],"</mml:semantics>":[82,142,180,230,243,256,295],"</mml:math>":[83,143,181,231,244,257,296],"</inline-formula>":[84,144,182,232,245,258,297],"alttext=\"upper":[90],"U":[91],"comma":[98,104,157],"<mml:mi>U</mml:mi>":[109],"<mml:mo>,</mml:mo>":[121,131,170],"encoding=\"application/x-tex\">U(a+\\epsilon":[137],"n,c+\\epsilon":[139],"n,z)</mml:annotation>":[141],",":[145,233,259],"where":[146],"alttext=\"epsilon":[151],"Subscript":[152],"i":[153],"equals":[155],"0":[156],"plus-or-minus":[158],"1\">":[159],"<mml:mi>i</mml:mi>":[166],"<mml:mo>=</mml:mo>":[168],"<mml:mn>0</mml:mn>":[169],"<mml:mo>":[171],"\u00b1":[172],"</mml:mo>":[173],"encoding=\"application/x-tex\">\\epsilon":[177],"_i=0,\\pm":[178],"1</mml:annotation>":[179],"(not":[183],"both":[184],"equal":[185],"to":[186],"0).":[187],"The":[188,213],"results":[189],"are":[190,215],"obtained":[191],"by":[192,202],"applying":[193],"Perron\u2019s":[194],"theorem,":[195],"together":[196],"with":[197,209,260],"uniform":[198],"asymptotic":[199],"estimates":[200],"derived":[201],"T.":[203],"M.":[204],"Dunster":[205],"Whittaker":[207],"large":[210],"parameter":[211],"values.":[212],"approximations":[214],"valid":[216],"complex":[218],"values":[219],"alttext=\"a\">":[225],"encoding=\"application/x-tex\">a</mml:annotation>":[229],"alttext=\"c\">":[238],"encoding=\"application/x-tex\">c</mml:annotation>":[242],"alttext=\"z\">":[251],"encoding=\"application/x-tex\">z</mml:annotation>":[255],"alttext=\"StartAbsoluteValue":[265],"arg":[266],"EndAbsoluteValue":[268],"greater-than":[269],"pi\">":[270],"<mml:mrow":[273,282],"class=\"MJX-TeXAtom-ORD\">":[274,283],"stretchy=\"false\">|</mml:mo>":[276,285],"<mml:mi>arg</mml:mi>":[278],"<mml:mspace":[279],"width=\"thinmathspace\"/>":[280],"<mml:mo>&gt;</mml:mo>":[287],"\u03c0":[289],"encoding=\"application/x-tex\">|\\arg":[293],"\\,z|&gt;\\pi</mml:annotation>":[294],".":[298]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}