{"id":"https://openalex.org/W2095333014","doi":"https://doi.org/10.1109/tcom.1984.1096009","title":"Series Representations for Rice's Ie Function","display_name":"Series Representations for Rice's Ie Function","publication_year":1984,"publication_date":"1984-12-01","ids":{"openalex":"https://openalex.org/W2095333014","doi":"https://doi.org/10.1109/tcom.1984.1096009","mag":"2095333014"},"language":"en","primary_location":{"id":"doi:10.1109/tcom.1984.1096009","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcom.1984.1096009","pdf_url":null,"source":{"id":"https://openalex.org/S4210170832","display_name":"IRE Transactions on Communications Systems","issn_l":"0096-2244","issn":["0096-2244","2162-2132"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Communications","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/A5073853778","display_name":"Benjamin Y. L. Tan","orcid":"https://orcid.org/0009-0002-9130-647X"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"B. Tan","raw_affiliation_strings":["Department of Electrical Engineering, National University of Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108512279","display_name":"T.T. Tjhung","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"T. Tjhung","raw_affiliation_strings":["Department of Electrical Engineering, National University of Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111874337","display_name":"Chin-Jit Teo","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"C. Teo","raw_affiliation_strings":["Department of Electrical Engineering, National University of Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037482622","display_name":"Wai Yie Leong","orcid":"https://orcid.org/0000-0002-5389-1121"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"P. Leong","raw_affiliation_strings":["Department of Electrical Engineering, National University of Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.276411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"32","issue":"12","first_page":"1342","last_page":"1344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987000226974487,"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":0.9987000226974487,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9840999841690063,"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/series","display_name":"Series (stratigraphy)","score":0.7396063208580017},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.6421526670455933},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5766770243644714},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48909956216812134},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4683394432067871},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45215344429016113},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4366515874862671},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41347068548202515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40981602668762207},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1262134611606598},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11657705903053284},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07659903168678284}],"concepts":[{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.7396063208580017},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.6421526670455933},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5766770243644714},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48909956216812134},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4683394432067871},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45215344429016113},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4366515874862671},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41347068548202515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40981602668762207},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1262134611606598},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11657705903053284},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07659903168678284},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcom.1984.1096009","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcom.1984.1096009","pdf_url":null,"source":{"id":"https://openalex.org/S4210170832","display_name":"IRE Transactions on Communications Systems","issn_l":"0096-2244","issn":["0096-2244","2162-2132"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Communications","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":5,"referenced_works":["https://openalex.org/W1556192255","https://openalex.org/W2018206532","https://openalex.org/W2142805181","https://openalex.org/W2168785037","https://openalex.org/W2986057930"],"related_works":["https://openalex.org/W2049939404","https://openalex.org/W1519777678","https://openalex.org/W2034875467","https://openalex.org/W76811607","https://openalex.org/W2265431734","https://openalex.org/W4388316559","https://openalex.org/W1848405970","https://openalex.org/W2011121568","https://openalex.org/W1607087086","https://openalex.org/W2144105040"],"abstract_inverted_index":{"Two":[0],"new":[1],"series":[2,18,34],"representations":[3],"for":[4,62],"the":[5,17,20,25,28,45],"Rice":[6],"function":[7],"<tex":[8,48,52],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,49,53],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Ie":[10],"(k,":[11],"x)</tex>":[12],"are":[13,60],"presented.":[14],"One":[15],"of":[16,44,47],"involves":[19,27],"modified":[21,29],"Struve":[22],"functions":[23,43],"and":[24,51,74],"other":[26,37],"Bessel":[30],"functions.":[31],"These":[32],"two":[33],"complement":[35],"each":[36],"in":[38],"their":[39],"convergence":[40],"speeds":[41],"as":[42],"values":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</tex>":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</tex>":[54],".":[55],"The":[56],"truncation":[57],"error":[58],"bounds":[59],"derived":[61],"both":[63],"series.":[64],"Therefore,":[65],"they":[66],"can":[67],"be":[68],"used":[69],"alternatively":[70],"with":[71],"high":[72],"efficiency":[73],"known":[75],"precision.":[76]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
