{"id":"https://openalex.org/W4401769272","doi":"https://doi.org/10.3390/a17080373","title":"Algorithms for Various Trigonometric Power Sums","display_name":"Algorithms for Various Trigonometric Power Sums","publication_year":2024,"publication_date":"2024-08-22","ids":{"openalex":"https://openalex.org/W4401769272","doi":"https://doi.org/10.3390/a17080373"},"language":"en","primary_location":{"id":"doi:10.3390/a17080373","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17080373","pdf_url":"https://www.mdpi.com/1999-4893/17/8/373/pdf?version=1724319706","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/17/8/373/pdf?version=1724319706","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086722977","display_name":"Victor Kowalenko","orcid":"https://orcid.org/0000-0002-7779-0042"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Victor Kowalenko","raw_affiliation_strings":["School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086722977"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.9912,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.73641315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"8","first_page":"373","last_page":"373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9977999925613403,"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":0.9977999925613403,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976999759674072,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9976000189781189,"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/trigonometry","display_name":"Trigonometry","score":0.7488935589790344},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.565131664276123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4846230447292328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44497740268707275},{"id":"https://openalex.org/keywords/pythagorean-trigonometric-identity","display_name":"Pythagorean trigonometric identity","score":0.433829665184021},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38360095024108887},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2052924633026123},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09473294019699097},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.08417236804962158},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05691143870353699}],"concepts":[{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.7488935589790344},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.565131664276123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4846230447292328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44497740268707275},{"id":"https://openalex.org/C89507098","wikidata":"https://www.wikidata.org/wiki/Q2039117","display_name":"Pythagorean trigonometric identity","level":5,"score":0.433829665184021},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38360095024108887},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2052924633026123},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09473294019699097},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.08417236804962158},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05691143870353699},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a17080373","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17080373","pdf_url":"https://www.mdpi.com/1999-4893/17/8/373/pdf?version=1724319706","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a6014db1b25d4260b4be0b704f8824b7","is_oa":true,"landing_page_url":"https://doaj.org/article/a6014db1b25d4260b4be0b704f8824b7","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 17, Iss 8, p 373 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/17/8/373/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a17080373","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a17080373","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a17080373","pdf_url":"https://www.mdpi.com/1999-4893/17/8/373/pdf?version=1724319706","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401769272.pdf","grobid_xml":"https://content.openalex.org/works/W4401769272.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W597057325","https://openalex.org/W1965857254","https://openalex.org/W2007342253","https://openalex.org/W2011195691","https://openalex.org/W2011219391","https://openalex.org/W2020842941","https://openalex.org/W2024762765","https://openalex.org/W2026231993","https://openalex.org/W2026870825","https://openalex.org/W2027274761","https://openalex.org/W2031224535","https://openalex.org/W2099389650","https://openalex.org/W2144480080","https://openalex.org/W2170576511","https://openalex.org/W2254580850","https://openalex.org/W2802074375","https://openalex.org/W4367369895","https://openalex.org/W6674713634"],"related_works":["https://openalex.org/W3022590230","https://openalex.org/W164200052","https://openalex.org/W4367369895","https://openalex.org/W1483355072","https://openalex.org/W579400037","https://openalex.org/W2550765215","https://openalex.org/W2125473902","https://openalex.org/W634571496","https://openalex.org/W4387010780","https://openalex.org/W3022244109"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"algorithms":[3],"for":[4,32],"different":[5],"types":[6,35],"of":[7,29,36,91,94,115,133,145],"trigonometric":[8,22,38,96,129,147],"power":[9,23,39,148],"sums":[10,24,40,51],"are":[11,136],"developed":[12],"and":[13,117],"presented.":[14],"Although":[15],"interesting":[16],"in":[17,42,48,57,71,88,98,104,113,123,149],"their":[18],"own":[19],"right,":[20],"these":[21,50,99,134],"arise":[25],"during":[26],"the":[27,33,43,84,89,92,95,105,118,124,128,143,146,150],"creation":[28],"an":[30],"algorithm":[31],"four":[34],"twisted":[37],"defined":[41],"introduction.":[44],"The":[45,131],"primary":[46],"aim":[47],"evaluating":[49],"is":[52],"to":[53,63,138],"obtain":[54,110],"exact":[55],"results":[56,70],"a":[58],"rational":[59],"form,":[60],"as":[61],"opposed":[62],"standard":[64],"or":[65],"direct":[66],"evaluation,":[67],"which":[68,152],"often":[69],"machine-dependent":[72],"decimal":[73],"values":[74],"that":[75,121],"can":[76,101,108],"be":[77,139,155],"affected":[78],"by":[79],"round-off":[80],"errors.":[81],"Moreover,":[82],"since":[83],"variable,":[85],"m,":[86],"appearing":[87],"denominators":[90],"arguments":[93],"functions":[97],"sums,":[100],"remain":[102],"algebraic":[103],"algorithms/codes,":[106],"one":[107],"also":[109],"polynomial":[111],"solutions":[112],"powers":[114],"m":[116],"variable":[119],"r":[120],"appears":[122],"cosine":[125],"factor":[126],"accompanying":[127],"power.":[130],"degrees":[132],"polynomials":[135],"found":[137],"dependent":[140],"upon":[141],"v,":[142],"value":[144],"sum,":[151],"must":[153],"always":[154],"specified.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}