{"id":"https://openalex.org/W1604646712","doi":"https://doi.org/10.1007/978-3-540-75187-8_1","title":"Analytic Solutions of Linear Difference Equations, Formal Series, and Bottom Summation","display_name":"Analytic Solutions of Linear Difference Equations, Formal Series, and Bottom Summation","publication_year":2007,"publication_date":"2007-09-01","ids":{"openalex":"https://openalex.org/W1604646712","doi":"https://doi.org/10.1007/978-3-540-75187-8_1","mag":"1604646712"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-75187-8_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-75187-8_1","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/A5066677758","display_name":"\u0421. \u0410. \u0410\u0431\u0440\u0430\u043c\u043e\u0432","orcid":null},"institutions":[{"id":"https://openalex.org/I2801535751","display_name":"Dorodnitsyn Computing Centre","ror":"https://ror.org/01vgda714","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801535751","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. A. Abramov","raw_affiliation_strings":["Russian Academy of Sciences, Dorodnicyn Computing Centre, Vavilova 40, 119991, Moscow GSP-1, Russia","Russian Academy of Sciences, Dorodnicyn Computing Centre, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Russian Academy of Sciences, Dorodnicyn Computing Centre, Vavilova 40, 119991, Moscow GSP-1, Russia","institution_ids":["https://openalex.org/I2801535751"]},{"raw_affiliation_string":"Russian Academy of Sciences, Dorodnicyn Computing Centre, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064920778","display_name":"Marko Petkov\u0161ek","orcid":"https://orcid.org/0000-0001-8629-350X"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"M. Petkov\u0161ek","raw_affiliation_strings":["University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 19, SI-1000 Ljubljana, Slovenia","University of Ljubljana, Faculty of mathematics and physics, Ljubljana, Slovenia"],"affiliations":[{"raw_affiliation_string":"University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 19, SI-1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"University of Ljubljana, Faculty of mathematics and physics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066677758"],"corresponding_institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I2801535751"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.1204,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81673307,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.9745000004768372,"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9745000004768372,"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/meromorphic-function","display_name":"Meromorphic function","score":0.8133233785629272},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.762648344039917},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6650339961051941},{"id":"https://openalex.org/keywords/euler-summation","display_name":"Euler summation","score":0.6644322872161865},{"id":"https://openalex.org/keywords/divergent-series","display_name":"Divergent series","score":0.617529034614563},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5645861625671387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4844944179058075},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4594598114490509},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4455844461917877},{"id":"https://openalex.org/keywords/borel-summation","display_name":"Borel summation","score":0.42962825298309326},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.4249576926231384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33400559425354004},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23632150888442993}],"concepts":[{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.8133233785629272},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.762648344039917},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6650339961051941},{"id":"https://openalex.org/C48330753","wikidata":"https://www.wikidata.org/wiki/Q374926","display_name":"Euler summation","level":5,"score":0.6644322872161865},{"id":"https://openalex.org/C120293249","wikidata":"https://www.wikidata.org/wiki/Q906520","display_name":"Divergent series","level":3,"score":0.617529034614563},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5645861625671387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4844944179058075},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4594598114490509},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4455844461917877},{"id":"https://openalex.org/C1033296","wikidata":"https://www.wikidata.org/wiki/Q2329388","display_name":"Borel summation","level":4,"score":0.42962825298309326},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.4249576926231384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33400559425354004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23632150888442993},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"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/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":2,"locations":[{"id":"doi:10.1007/978-3-540-75187-8_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-75187-8_1","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.579.7490","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.579.7490","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ccas.ru/sabramov/ps/afsFinal16_07.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W73298482","https://openalex.org/W1977660677","https://openalex.org/W2029108302","https://openalex.org/W2036893080","https://openalex.org/W2083121165","https://openalex.org/W2094144431","https://openalex.org/W2153531485","https://openalex.org/W2495327222","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2263926104","https://openalex.org/W4300687355","https://openalex.org/W2076429287","https://openalex.org/W2041779119","https://openalex.org/W2390547203","https://openalex.org/W2561226310","https://openalex.org/W2247535618","https://openalex.org/W2229193568","https://openalex.org/W2257017810","https://openalex.org/W2755106522"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}