{"id":"https://openalex.org/W1985953447","doi":"https://doi.org/10.1137/s003614109935050x","title":"A Monotonicity Property Involving <sub>3</sub><i>F</i><sub>2</sub> and Comparisons of the Classical Approximations of Elliptical Arc Length","display_name":"A Monotonicity Property Involving <sub>3</sub><i>F</i><sub>2</sub> and Comparisons of the Classical Approximations of Elliptical Arc Length","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1985953447","doi":"https://doi.org/10.1137/s003614109935050x","mag":"1985953447"},"language":"en","primary_location":{"id":"doi:10.1137/s003614109935050x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614109935050x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical 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/A5024937255","display_name":"Roger Barnard","orcid":"https://orcid.org/0000-0002-0538-7158"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Roger W. Barnard","raw_affiliation_strings":["Department of Mathematics, Texas Tech University, Lubbock, TX 79409"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas Tech University, Lubbock, TX 79409","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058801422","display_name":"Kent Pearce","orcid":null},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kent Pearce","raw_affiliation_strings":["Department of Mathematics, Texas Tech University, Lubbock, TX 79409"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas Tech University, Lubbock, TX 79409","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046225045","display_name":"Kendall C. Richards","orcid":"https://orcid.org/0000-0002-7424-5129"},"institutions":[{"id":"https://openalex.org/I8616870","display_name":"Southwestern University","ror":"https://ror.org/05gj63w50","country_code":"US","type":"education","lineage":["https://openalex.org/I8616870"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kendall C. Richards","raw_affiliation_strings":["Department of Mathematics, Southwestern University, Georgetown, TX 78626"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southwestern University, Georgetown, TX 78626","institution_ids":["https://openalex.org/I8616870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024937255"],"corresponding_institution_ids":["https://openalex.org/I12315562"],"apc_list":null,"apc_paid":null,"fwci":1.1282,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.73411829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"2","first_page":"403","last_page":"419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9980999827384949,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9980999827384949,"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":0.9980000257492065,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9966999888420105,"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":0.8095626831054688},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6456784009933472},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.567327618598938},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.4834495484828949},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.47767123579978943},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.45830607414245605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3688247799873352},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26834428310394287}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8095626831054688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6456784009933472},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.567327618598938},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.4834495484828949},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.47767123579978943},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.45830607414245605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3688247799873352},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26834428310394287}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s003614109935050x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614109935050x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.297.1754","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.1754","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ttu.edu/~pearce/papers/classic.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W647745059","https://openalex.org/W658266689","https://openalex.org/W1969129084","https://openalex.org/W1977177541","https://openalex.org/W1987677613","https://openalex.org/W1993407479","https://openalex.org/W2008052995","https://openalex.org/W2017221560","https://openalex.org/W2031075135","https://openalex.org/W2033923703","https://openalex.org/W2047643486","https://openalex.org/W2120062331"],"related_works":["https://openalex.org/W2951610245","https://openalex.org/W2795079910","https://openalex.org/W1430963189","https://openalex.org/W2052430123","https://openalex.org/W3037410748","https://openalex.org/W2049901819","https://openalex.org/W1489292980","https://openalex.org/W4319835971","https://openalex.org/W2278426376","https://openalex.org/W1983437306"],"abstract_inverted_index":{"Conditions":[0],"are":[1],"determined":[2],"under":[3],"which":[4,108],"$":[5],"\\,_{3}F_{2}\\left(-n,a,b;a+b+2,\\varepsilon":[6],"-n+1;1\\right)$":[7],"is":[8,65],"a":[9,19,23],"monotone":[10],"function":[11],"of":[12,25,28,78,82,88,95,101,103],"n":[13],"satisfying":[14],"$a":[15],"b\\cdot\\,_{3}F_{2}\\left(-n,a,b;a+b+2,\\varepsilon":[16],"-n+1;1\\right)":[17],"\\geq":[18,57],"b\\cdot\\,_{2}F_{1}\\left(a,b;a+b+2;1\\right).$":[20],"Motivated":[21],"by":[22],"conjecture":[24],"Vuorinen":[26],"[Proceedings":[27],"Special":[29],"Functions":[30],"and":[31,62,129],"Differential":[32],"Equations,":[33],"K.":[34],"S.":[35],"Rao,":[36],"R.":[37],"Jagannathan,":[38],"G.":[39],"Vanden":[40],"Berghe,":[41],"J.":[42],"Van":[43],"der":[44],"Jeugt,":[45],"eds.,":[46],"Allied":[47],"Publishers,":[48],"New":[49],"Delhi,":[50],"1998],":[51],"the":[52,73,79,91,99,104],"corollary":[53],"that":[54],"$\\,_{3}F_{2}(-n,-\\frac{1}{2},-\\frac{1}{2};1,\\varepsilon":[55],"-n+1;1)":[56],"\\frac{4}{\\pi},$":[58],"for":[59,107],"$1>\\epsilon":[60],"\\geq\\frac{1}{4}$":[61],"$n\\geq":[63],"2,$":[64],"used":[66],"to":[67,125],"determine":[68],"surprising":[69],"hierarchical":[70],"relationships":[71],"among":[72],"13":[74],"known":[75,105],"historical":[76],"approximations":[77,116],"arc":[80],"length":[81],"an":[83],"ellipse.":[84],"This":[85],"complete":[86],"list":[87],"inequalities":[89],"compares":[90],"Maclaurin":[92],"series":[93],"coefficients":[94,100],"2F1":[96],",":[97],"with":[98],"each":[102],"approximations,":[106],"maximum":[109],"errors":[110],"can":[111],"then":[112],"be":[113],"established.":[114],"These":[115],"range":[117],"over":[118],"four":[119],"centuries":[120],"from":[121,132],"Kepler's":[122],"in":[123,127],"1609":[124],"Almkvist's":[126],"1985":[128],"include":[130],"two":[131],"Ramanujan.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
