{"id":"https://openalex.org/W4380608831","doi":"https://doi.org/10.1090/mcom/3874","title":"Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity","display_name":"Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity","publication_year":2023,"publication_date":"2023-06-14","ids":{"openalex":"https://openalex.org/W4380608831","doi":"https://doi.org/10.1090/mcom/3874"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3874","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1090/mcom/3874","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057705484","display_name":"Dmitrii Karp","orcid":"https://orcid.org/0000-0001-8206-3539"},"institutions":[{"id":"https://openalex.org/I157943965","display_name":"Holon Institute of Technology","ror":"https://ror.org/02prqh017","country_code":"IL","type":"education","lineage":["https://openalex.org/I157943965"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Dmitrii Karp","raw_affiliation_strings":["Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel","institution_ids":["https://openalex.org/I157943965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100388128","display_name":"Yi Zhang","orcid":"https://orcid.org/0000-0002-2367-2497"},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Zhang","raw_affiliation_strings":["Department of Foundational Mathematics, School of Mathematics and Physics, Xi\u00e2\u0080\u0099an Jiaotong-Liverpool University, Suzhou 215123, People\u00e2\u0080\u0099s Republic of China","Department of Foundational Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Foundational Mathematics, School of Mathematics and Physics, Xi\u00e2\u0080\u0099an Jiaotong-Liverpool University, Suzhou 215123, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I69356397"]},{"raw_affiliation_string":"Department of Foundational Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, People\u2019s Republic of China","institution_ids":["https://openalex.org/I69356397"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057705484"],"corresponding_institution_ids":["https://openalex.org/I157943965"],"apc_list":null,"apc_paid":null,"fwci":1.0377,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.712818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"92","issue":"344","first_page":"2769","last_page":"2794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9994000196456909,"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/T12508","display_name":"Functional Equations Stability Results","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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6070070266723633},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4312623143196106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36982858180999756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3521556854248047}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6070070266723633},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4312623143196106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36982858180999756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3521556854248047}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3874","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1090/mcom/3874","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1311863243","display_name":null,"funder_award_id":"RDF-20-01-12","funder_id":"https://openalex.org/F4320324032","funder_display_name":"Xi\u2019an Jiaotong-Liverpool University"},{"id":"https://openalex.org/G1330707645","display_name":null,"funder_award_id":"21KJB110032","funder_id":"https://openalex.org/F4320327891","funder_display_name":"Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions"},{"id":"https://openalex.org/G1393905553","display_name":null,"funder_award_id":"21KJB110032","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3301728482","display_name":null,"funder_award_id":"RDF-20-01-12","funder_id":"https://openalex.org/F4320327891","funder_display_name":"Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions"},{"id":"https://openalex.org/G3963755327","display_name":null,"funder_award_id":"12101506","funder_id":"https://openalex.org/F4320324032","funder_display_name":"Xi\u2019an Jiaotong-Liverpool University"},{"id":"https://openalex.org/G5699341605","display_name":null,"funder_award_id":"RDF-20-01-12","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G679200776","display_name":null,"funder_award_id":"12101506","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7957294185","display_name":null,"funder_award_id":"12101506","funder_id":"https://openalex.org/F4320327891","funder_display_name":"Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions"},{"id":"https://openalex.org/G8110964859","display_name":null,"funder_award_id":"21KJB110032","funder_id":"https://openalex.org/F4320324032","funder_display_name":"Xi\u2019an Jiaotong-Liverpool University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324032","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05"},{"id":"https://openalex.org/F4320327891","display_name":"Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1574149470","https://openalex.org/W1982792721","https://openalex.org/W2000928349","https://openalex.org/W2003504038","https://openalex.org/W2007395843","https://openalex.org/W2027384932","https://openalex.org/W2044566390","https://openalex.org/W2053120655","https://openalex.org/W2090142727","https://openalex.org/W2094965692","https://openalex.org/W2143273410","https://openalex.org/W2148424441","https://openalex.org/W2316478233","https://openalex.org/W2324354372","https://openalex.org/W2615988577","https://openalex.org/W4237803684","https://openalex.org/W4289981527","https://openalex.org/W4300694852"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0],"find":[1],"two":[2],"series":[3,267],"expansions":[4,48,91],"for":[5,213,252],"Legendre\u2019s":[6],"second":[7],"incomplete":[8],"elliptic":[9],"integral":[10],"<inline-formula":[11,59,98,130,143,165,214],"content-type=\"math/mathml\">":[12,60,99,131,144,166,215],"<mml:math":[13,61,100,132,145,167,216],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,62,101,133,146,168,217],"alttext=\"upper":[15,102,218],"E":[16,103,219],"left-parenthesis":[17,104,220],"lamda":[18,64,105,221],"comma":[19,65,106,222],"k":[20,66,107,171,223],"right-parenthesis\">":[21,67,108,224],"<mml:semantics>":[22,68,109,135,148,174,225],"<mml:mrow>":[23,69,110,175,226],"<mml:mi>E</mml:mi>":[24,111,227],"<mml:mo":[25,30,70,75,112,117,228,233],"stretchy=\"false\">(</mml:mo>":[26,71,113,229],"<mml:mi>\u03bb</mml:mi>":[27,72,114,136,176,230],"<mml:mo>,</mml:mo>":[28,73,115,231],"<mml:mi>k</mml:mi>":[29,74,116,149,178,232],"stretchy=\"false\">)</mml:mo>":[31,76,118,234],"</mml:mrow>":[32,77,119,181,235],"<mml:annotation":[33,78,120,137,150,182,236],"encoding=\"application/x-tex\">E(\\lambda":[34,121,237],",":[35,80,238],"k)</mml:annotation>":[36,81,239],"</mml:semantics>":[37,82,123,139,152,185,240],"</mml:math>":[38,83,124,140,153,186,241],"</inline-formula>":[39,84,125,141,154,187],"in":[40,57],"terms":[41],"of":[42,53,88,95,206,275,278],"recursively":[43],"computed":[44],"elementary":[45],"functions.":[46],"Both":[47],"converge":[49],"at":[50,197],"every":[51],"point":[52],"the":[54,58,89,162,244,276,279],"unit":[55],"square":[56],"alttext=\"left-parenthesis":[63],"encoding=\"application/x-tex\">(\\lambda":[79],"plane.":[85],"Partial":[86],"sums":[87],"proposed":[90],"form":[92],"a":[93,204],"sequence":[94,205],"approximations":[96,254],"to":[97,156,258],",k)</mml:annotation>":[122],"which":[126],"are":[127,195,264],"asymptotic":[128],"when":[129,159],"alttext=\"lamda\">":[134],"encoding=\"application/x-tex\">\\lambda</mml:annotation>":[138],"and/or":[142],"alttext=\"k\">":[147],"encoding=\"application/x-tex\">k</mml:annotation>":[151],"tend":[155],"unity,":[157],"including":[158,283],"both":[160],"approach":[161],"logarithmic":[163],"singularity":[164],"alttext=\"lamda":[169],"equals":[170,172],"1\">":[173],"<mml:mo>=</mml:mo>":[177,179],"<mml:mn>1</mml:mn>":[180],"encoding=\"application/x-tex\">\\lambda":[183],"=k=1</mml:annotation>":[184],"from":[188],"any":[189],"direction.":[190],"Explicit":[191],"two-sided":[192,211],"error":[193],"bounds":[194,202],"given":[196],"each":[198],"approximation":[199],"order.":[200],"These":[201],"yield":[203],"increasingly":[207],"precise":[208],"asymptotically":[209],"correct":[210],"inequalities":[212],"</inline-formula>.":[242],"For":[243],"reader\u2019s":[245],"convenience":[246],"we":[247],"further":[248],"present":[249],"explicit":[250],"expressions":[251],"low-order":[253],"and":[255,272],"numerical":[256],"examples":[257],"illustrate":[259],"their":[260],"accuracy.":[261],"Our":[262],"derivations":[263],"based":[265],"on":[266],"rearrangements,":[268],"hypergeometric":[269,281],"summation":[270],"algorithms":[271],"extensive":[273],"use":[274],"properties":[277],"generalized":[280],"functions":[282],"some":[284],"recent":[285],"inequalities.":[286]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}