{"id":"https://openalex.org/W2053811128","doi":"https://doi.org/10.1137/0218061","title":"An Analysis of the Rational Exponential Integral","display_name":"An Analysis of the Rational Exponential Integral","publication_year":1989,"publication_date":"1989-10-01","ids":{"openalex":"https://openalex.org/W2053811128","doi":"https://doi.org/10.1137/0218061","mag":"2053811128"},"language":"en","primary_location":{"id":"doi:10.1137/0218061","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218061","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5052550406","display_name":"Guy W. Cherry","orcid":null},"institutions":[{"id":"https://openalex.org/I1282770075","display_name":"Tektronix (United States)","ror":"https://ror.org/04kw5s604","country_code":"US","type":"company","lineage":["https://openalex.org/I1282770075"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. W. Cherry","raw_affiliation_strings":["Tektronix Labs, Beaverton, OR#TAB#"],"affiliations":[{"raw_affiliation_string":"Tektronix Labs, Beaverton, OR#TAB#","institution_ids":["https://openalex.org/I1282770075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052550406"],"corresponding_institution_ids":["https://openalex.org/I1282770075"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.19585322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"5","first_page":"893","last_page":"905"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9581999778747559,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9581999778747559,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9350000023841858,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/rational-function","display_name":"Rational function","score":0.715766191482544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7014868259429932},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.6904834508895874},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6440823674201965},{"id":"https://openalex.org/keywords/elementary-function","display_name":"Elementary function","score":0.6412402987480164},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5760799646377563},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5585402846336365},{"id":"https://openalex.org/keywords/special-functions","display_name":"Special functions","score":0.5162944197654724},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4952155649662018},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.48854050040245056},{"id":"https://openalex.org/keywords/exponential-integral","display_name":"Exponential integral","score":0.46856242418289185},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.42356163263320923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41722187399864197},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3750796914100647},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3596641421318054},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3342001736164093},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30379998683929443},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.23322883248329163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21620845794677734},{"id":"https://openalex.org/keywords/volume-integral","display_name":"Volume integral","score":0.10057735443115234},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07807940244674683}],"concepts":[{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.715766191482544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7014868259429932},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.6904834508895874},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6440823674201965},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.6412402987480164},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5760799646377563},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5585402846336365},{"id":"https://openalex.org/C50757856","wikidata":"https://www.wikidata.org/wiki/Q867707","display_name":"Special functions","level":2,"score":0.5162944197654724},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4952155649662018},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.48854050040245056},{"id":"https://openalex.org/C53819440","wikidata":"https://www.wikidata.org/wiki/Q1419948","display_name":"Exponential integral","level":4,"score":0.46856242418289185},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.42356163263320923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41722187399864197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3750796914100647},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3596641421318054},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3342001736164093},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30379998683929443},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.23322883248329163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21620845794677734},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.10057735443115234},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07807940244674683},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0218061","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218061","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W104828541","https://openalex.org/W1989461817","https://openalex.org/W2006090934","https://openalex.org/W2021106850","https://openalex.org/W2037327216","https://openalex.org/W2077956756","https://openalex.org/W2089728300","https://openalex.org/W2140443967","https://openalex.org/W3046782287"],"related_works":["https://openalex.org/W4253900131","https://openalex.org/W1877027850","https://openalex.org/W564617080","https://openalex.org/W1663513604","https://openalex.org/W2495607074","https://openalex.org/W4233994338","https://openalex.org/W2037327216","https://openalex.org/W4210963063","https://openalex.org/W2053811128","https://openalex.org/W2031048748"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"an":[3,66],"algorithm":[4,62,83,134],"is":[5,65,158],"presented":[6,63],"for":[7,72],"integrating":[8,73],"expressions":[9],"of":[10,23,27,30,42,107,119,141,155],"the":[11,34,46,49,52,58,78,86,104,124,142],"form":[12],"$\\smallint":[13],"ge^f":[14],"dx$,":[15],"where":[16],"f":[17],"and":[18,54,57],"g":[19],"are":[20],"rational":[21],"functions":[22,32,44,76,89],"x,":[24],"in":[25,77,122],"terms":[26],"a":[28,151],"class":[29,41],"special":[31,35,43,75,88],"called":[33],"incomplete":[36],"$\\Gamma":[37],"$":[38],"functions.":[39],"This":[40,82,112,133],"includes":[45],"exponential":[47],"integral,":[48],"error":[50],"function,":[51],"sine":[53],"cosine":[55],"integrals,":[56],"Fresnel":[59],"integrals.":[60],"The":[61],"here":[64],"improvement":[67],"over":[68,116],"those":[69],"published":[70],"previously":[71,94],"with":[74],"following":[79],"ways:":[80],"(i)":[81],"combines":[84],"all":[85],"above":[87],"into":[90],"one":[91],"algorithm,":[92,113],"whereas":[93],"they":[95],"were":[96],"treated":[97],"separately.":[98],"(ii)":[99],"Previous":[100],"algorithms":[101],"require":[102],"that":[103],"underlying":[105],"field":[106,118,126],"constants":[108],"be":[109,129],"algebraically":[110],"closed.":[111],"however,":[114],"works":[115],"any":[117],"characteristic":[120],"zero":[121],"which":[123],"basic":[125],"operations":[127],"can":[128],"carried":[130],"out.":[131],"(iii)":[132],"does":[135],"not":[136],"rely":[137],"on":[138],"Risch\u2019s":[139],"solution":[140],"differential":[143],"equation":[144],"$y'":[145],"+":[146],"fy":[147],"=":[148],"g$.":[149],"Instead,":[150],"more":[152],"direct":[153],"method":[154],"undetermined":[156],"coefficients":[157],"used.":[159]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}