{"id":"https://openalex.org/W2044566390","doi":"https://doi.org/10.1137/s0036141099351176","title":"Asymptotic Expansions of Symmetric Standard Elliptic Integrals","display_name":"Asymptotic Expansions of Symmetric Standard Elliptic Integrals","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2044566390","doi":"https://doi.org/10.1137/s0036141099351176","mag":"2044566390"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141099351176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141099351176","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/A5026128180","display_name":"Jos\u00e9 L. L\u00f3pez","orcid":"https://orcid.org/0000-0002-6050-9015"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jos\u00e9 L. L\u00f3pez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5026128180"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7709,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.82825697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"4","first_page":"754","last_page":"775"},"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/T10514","display_name":"Numerical methods in engineering","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9926000237464905,"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":0.9035053253173828},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.7131907343864441},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6147170066833496},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6037744283676147},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5335384607315063},{"id":"https://openalex.org/keywords/elliptic-integral","display_name":"Elliptic integral","score":0.5071845054626465},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.499370813369751},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.485058456659317},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.4744737446308136},{"id":"https://openalex.org/keywords/method-of-matched-asymptotic-expansions","display_name":"Method of matched asymptotic expansions","score":0.46969059109687805},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4135745167732239},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3380679488182068},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1462228000164032},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07364842295646667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9035053253173828},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.7131907343864441},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6147170066833496},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6037744283676147},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5335384607315063},{"id":"https://openalex.org/C52704855","wikidata":"https://www.wikidata.org/wiki/Q1126603","display_name":"Elliptic integral","level":2,"score":0.5071845054626465},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.499370813369751},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.485058456659317},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.4744737446308136},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.46969059109687805},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4135745167732239},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3380679488182068},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1462228000164032},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07364842295646667},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141099351176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141099351176","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1974945857","https://openalex.org/W1982792721","https://openalex.org/W2007395843","https://openalex.org/W2025212173","https://openalex.org/W2039697007","https://openalex.org/W2043129690","https://openalex.org/W2051068839","https://openalex.org/W2052552439","https://openalex.org/W2057817591","https://openalex.org/W2061411896","https://openalex.org/W2066824107","https://openalex.org/W2067077963","https://openalex.org/W2081633643","https://openalex.org/W2088656168","https://openalex.org/W2092997395","https://openalex.org/W2106341564","https://openalex.org/W2170706425","https://openalex.org/W2324354372","https://openalex.org/W3016843226","https://openalex.org/W4239265288","https://openalex.org/W4285719527","https://openalex.org/W4298053401"],"related_works":["https://openalex.org/W2947785198","https://openalex.org/W193857389","https://openalex.org/W2123200440","https://openalex.org/W2019314278","https://openalex.org/W4247062277","https://openalex.org/W2380855050","https://openalex.org/W2150724252","https://openalex.org/W4387947628","https://openalex.org/W1984487343","https://openalex.org/W2127104884"],"abstract_inverted_index":{"Symmetric":[0],"standard":[1],"elliptic":[2],"integrals":[3,28],"are":[4,56,67,106],"considered":[5],"when":[6],"one":[7],"of":[8,26,32,40,53,71,76,86,88,115],"their":[9],"parameters":[10],"is":[11,19],"larger":[12],"than":[13],"the":[14,33,49,61,77,96,100,104,116],"others.":[15],"The":[16,83],"distributional":[17],"approach":[18],"used":[20],"for":[21,92],"deriving":[22],"five":[23,35],"convergent":[24],"expansions":[25,42,55,64,90,105],"these":[27,41,54,65,89],"in":[29,48,69],"inverse":[30],"powers":[31],"respective":[34],"possible":[36],"asymptotic":[37,50,97],"parameters.":[38],"Four":[39],"also":[43],"involve":[44,80],"a":[45],"logarithmic":[46],"term":[47],"variable.":[51],"Coefficients":[52],"obtained":[57],"by":[58,108],"recurrence.":[59],"For":[60],"first":[62],"four":[63],"coefficients":[66,75],"expressed":[68],"terms":[70],"elementary":[72],"functions,":[73],"whereas":[74],"fifth":[78],"expansion":[79],"nonelementary":[81],"functions.":[82],"convergence":[84],"speed":[85],"any":[87,113],"increases":[91],"increasing":[93],"difference":[94],"between":[95],"variable":[98],"and":[99],"remaining":[101],"ones.":[102],"All":[103],"accompanied":[107],"an":[109],"error":[110],"bound":[111],"at":[112],"order":[114],"approximation.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}