{"id":"https://openalex.org/W1522380943","doi":"https://doi.org/10.1007/3-540-15984-3_335","title":"Elementary and Liouvillian solutions of linear differential equations","display_name":"Elementary and Liouvillian solutions of linear differential equations","publication_year":1985,"publication_date":"1985-01-01","ids":{"openalex":"https://openalex.org/W1522380943","doi":"https://doi.org/10.1007/3-540-15984-3_335","mag":"1522380943"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-15984-3_335","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-15984-3_335","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/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":["Dept. of Mathematics, North Carolina State University, 27695-8205, Raleigh, NC","Department of Mathematics, North Carolina State University, Raleigh,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, North Carolina State University, 27695-8205, Raleigh, NC","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh,","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","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","School of Mathematics University of Bath 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"]},{"raw_affiliation_string":"School of Mathematics University of Bath Bath, England","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.20141343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"595","last_page":"596"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9128999710083008,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9128999710083008,"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/computer-science","display_name":"Computer science","score":0.7013810276985168},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.545576810836792},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48499271273612976},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.4365331530570984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3494842052459717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20536592602729797},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18671366572380066}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7013810276985168},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.545576810836792},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48499271273612976},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.4365331530570984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3494842052459717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20536592602729797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18671366572380066}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-15984-3_335","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-15984-3_335","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1980662086","https://openalex.org/W1987081771","https://openalex.org/W1991317883","https://openalex.org/W2022258640","https://openalex.org/W2026131803","https://openalex.org/W2037327216","https://openalex.org/W2040655168","https://openalex.org/W2042453305","https://openalex.org/W2073681010","https://openalex.org/W2081160235","https://openalex.org/W2083715119","https://openalex.org/W2140443967","https://openalex.org/W2317024018","https://openalex.org/W2370045957"],"related_works":["https://openalex.org/W2347435260","https://openalex.org/W2353151757","https://openalex.org/W2349831920","https://openalex.org/W2001617949","https://openalex.org/W2363313804","https://openalex.org/W2573515625","https://openalex.org/W2387425078","https://openalex.org/W2519311886","https://openalex.org/W283818205","https://openalex.org/W2348403575"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}