{"id":"https://openalex.org/W2810056370","doi":"https://doi.org/10.1007/s00211-018-0978-y","title":"An alternative to the Euler\u2013Maclaurin summation formula: approximating sums by integrals only","display_name":"An alternative to the Euler\u2013Maclaurin summation formula: approximating sums by integrals only","publication_year":2018,"publication_date":"2018-06-28","ids":{"openalex":"https://openalex.org/W2810056370","doi":"https://doi.org/10.1007/s00211-018-0978-y","mag":"2810056370"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-018-0978-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-018-0978-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5058378725","display_name":"Iosif Pinelis","orcid":"https://orcid.org/0000-0003-4742-5789"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Iosif Pinelis","raw_affiliation_strings":["Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA","institution_ids":["https://openalex.org/I11957088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058378725"],"corresponding_institution_ids":["https://openalex.org/I11957088"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.8271,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83832194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"140","issue":"3","first_page":"755","last_page":"790"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.998199999332428,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8138290643692017},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.6321814656257629},{"id":"https://openalex.org/keywords/euler-summation","display_name":"Euler summation","score":0.6288266181945801},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5393168330192566},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.5316040515899658},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5045682191848755},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4973476231098175},{"id":"https://openalex.org/keywords/polylogarithm","display_name":"Polylogarithm","score":0.47542908787727356},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.446178674697876},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.44222575426101685},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4369211792945862},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38392797112464905},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3535480797290802},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2571495771408081},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.24982419610023499},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.1730024218559265},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.08088967204093933}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8138290643692017},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.6321814656257629},{"id":"https://openalex.org/C48330753","wikidata":"https://www.wikidata.org/wiki/Q374926","display_name":"Euler summation","level":5,"score":0.6288266181945801},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5393168330192566},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.5316040515899658},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5045682191848755},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4973476231098175},{"id":"https://openalex.org/C186934003","wikidata":"https://www.wikidata.org/wiki/Q1238449","display_name":"Polylogarithm","level":5,"score":0.47542908787727356},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.446178674697876},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.44222575426101685},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4369211792945862},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38392797112464905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3535480797290802},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2571495771408081},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.24982419610023499},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.1730024218559265},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.08088967204093933},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C71897612","wikidata":"https://www.wikidata.org/wiki/Q1896470","display_name":"Prime zeta function","level":4,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"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/s00211-018-0978-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-018-0978-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p-23957","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/4655","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1592261758","https://openalex.org/W1600201693","https://openalex.org/W1805871248","https://openalex.org/W1970404983","https://openalex.org/W1974330326","https://openalex.org/W2000977329","https://openalex.org/W2007225893","https://openalex.org/W2029949308","https://openalex.org/W2156023017","https://openalex.org/W2397234481","https://openalex.org/W2499779551","https://openalex.org/W2625775094","https://openalex.org/W2963907200","https://openalex.org/W4233185505","https://openalex.org/W4236419838","https://openalex.org/W4238900504","https://openalex.org/W4255050078","https://openalex.org/W4302050383"],"related_works":["https://openalex.org/W68100126","https://openalex.org/W2263926104","https://openalex.org/W4297814030","https://openalex.org/W3124095481","https://openalex.org/W3216251873","https://openalex.org/W4300687355","https://openalex.org/W3106493317","https://openalex.org/W2546979858","https://openalex.org/W2390547203","https://openalex.org/W2810056370"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
