{"id":"https://openalex.org/W2124423029","doi":"https://doi.org/10.1016/s0747-7171(86)80026-8","title":"Elementary and Liouvillian Solutions of Linear Differential Equations","display_name":"Elementary and Liouvillian Solutions of Linear Differential Equations","publication_year":1986,"publication_date":"1986-09-01","ids":{"openalex":"https://openalex.org/W2124423029","doi":"https://doi.org/10.1016/s0747-7171(86)80026-8","mag":"2124423029"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(86)80026-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(86)80026-8","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic 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/A5043054372","display_name":"James H. Davenport","orcid":"https://orcid.org/0000-0002-3982-7545"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J.H. Davenport","raw_affiliation_strings":["School of Mathematics, University of Bath, Claverton Down, Bath, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Bath, Claverton Down, Bath, England","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071271321","display_name":"Michael F. Singer","orcid":"https://orcid.org/0000-0001-6526-8313"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M.F. Singer","raw_affiliation_strings":["Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, U.S.A","Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, U.S.A.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, U.S.A","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, U.S.A.#TAB#","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2770,"currency":"USD","value_usd":2770},"apc_paid":null,"fwci":2.4737,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.89874064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":"3","first_page":"237","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9959999918937683,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9959999918937683,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9735000133514404,"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":0.8871704339981079},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.7372791767120361},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.616888701915741},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5555346012115479},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5549870729446411},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5348395705223083},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.5211994051933289},{"id":"https://openalex.org/keywords/algebraic-differential-equation","display_name":"Algebraic differential equation","score":0.4784403145313263},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4442322850227356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44042250514030457},{"id":"https://openalex.org/keywords/algebraic-element","display_name":"Algebraic element","score":0.4203642010688782},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36804941296577454},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36669492721557617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31155043840408325},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.2145729660987854},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.15579435229301453},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.061288982629776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8871704339981079},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.7372791767120361},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.616888701915741},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5555346012115479},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5549870729446411},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5348395705223083},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.5211994051933289},{"id":"https://openalex.org/C97145343","wikidata":"https://www.wikidata.org/wiki/Q4723995","display_name":"Algebraic differential equation","level":5,"score":0.4784403145313263},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4442322850227356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44042250514030457},{"id":"https://openalex.org/C173832452","wikidata":"https://www.wikidata.org/wiki/Q162608","display_name":"Algebraic element","level":5,"score":0.4203642010688782},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36804941296577454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36669492721557617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31155043840408325},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2145729660987854},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.15579435229301453},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.061288982629776},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0747-7171(86)80026-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(86)80026-8","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","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":17,"referenced_works":["https://openalex.org/W1585998846","https://openalex.org/W1874323780","https://openalex.org/W1980662086","https://openalex.org/W1987081771","https://openalex.org/W1991317883","https://openalex.org/W2026131803","https://openalex.org/W2037327216","https://openalex.org/W2040655168","https://openalex.org/W2073681010","https://openalex.org/W2081160235","https://openalex.org/W2083715119","https://openalex.org/W2140443967","https://openalex.org/W2317024018","https://openalex.org/W2370045957","https://openalex.org/W4236394708","https://openalex.org/W4285259853","https://openalex.org/W6660443693"],"related_works":["https://openalex.org/W2603064975","https://openalex.org/W1512363145","https://openalex.org/W2046049376","https://openalex.org/W4381514690","https://openalex.org/W2061175295","https://openalex.org/W4280616957","https://openalex.org/W2963835463","https://openalex.org/W2895122765","https://openalex.org/W2950272280","https://openalex.org/W2124423029"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
