{"id":"https://openalex.org/W7225252400","doi":"https://doi.org/10.5281/zenodo.23958816","title":"A High-Precision Approximation to \ud835\udf0b using a Trigonometric Limiting Sequence","display_name":"A High-Precision Approximation to \ud835\udf0b using a Trigonometric Limiting Sequence","publication_year":2026,"publication_date":"2026-11-04","ids":{"openalex":"https://openalex.org/W7225252400","doi":"https://doi.org/10.5281/zenodo.23958816"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23958816","doi":"https://doi.org/10.5281/zenodo.23958816","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23958816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23958816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148777753","display_name":"Bheema Varanasi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Varanasi, Bheema","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0006-1805-1860","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148777753"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.5648999810218811,"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":0.5648999810218811,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.12349999696016312,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12504","display_name":"Mathematics and Applications","score":0.11159999668598175,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7563999891281128},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7174999713897705},{"id":"https://openalex.org/C120362076","wikidata":"https://www.wikidata.org/wiki/Q1149336","display_name":"Trigonometric series","level":2,"score":0.7021999955177307},{"id":"https://openalex.org/C30786353","wikidata":"https://www.wikidata.org/wiki/Q3296857","display_name":"Differentiation of trigonometric functions","level":5,"score":0.6039999723434448},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.54830002784729},{"id":"https://openalex.org/C89507098","wikidata":"https://www.wikidata.org/wiki/Q2039117","display_name":"Pythagorean trigonometric identity","level":5,"score":0.545199990272522},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5367000102996826},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.49410000443458557},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C65692021","wikidata":"https://www.wikidata.org/wiki/Q1094282","display_name":"Trigonometric integral","level":3,"score":0.47589999437332153},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.3878999948501587},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.328000009059906},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3190999925136566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3156999945640564},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C9317044","wikidata":"https://www.wikidata.org/wiki/Q1191963","display_name":"Trigonometric substitution","level":5,"score":0.27570000290870667},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C65454745","wikidata":"https://www.wikidata.org/wiki/Q6043250","display_name":"Integration using Euler's formula","level":5,"score":0.26190000772476196},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2590000033378601}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.23958816","doi":"https://doi.org/10.5281/zenodo.23958816","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23958816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23958817","doi":"https://doi.org/10.5281/zenodo.23958817","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23958817","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23963217","doi":"https://doi.org/10.5281/zenodo.23963217","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23963217","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23958816","doi":"https://doi.org/10.5281/zenodo.23958816","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23958816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"note":[1],"introduces":[2],"a":[3],"closed-form":[4],"transcendental":[5],"sequence":[6],"that":[7],"converges":[8],"monotonically":[9],"to":[10],"\ud835\udf0b,":[11],"constructed":[12],"by":[13],"embedding":[14],"an":[15,21],"base-10":[16],"infinite":[17],"geometric":[18],"series":[19],"within":[20],"inverse":[22],"trigonometric":[23],"operator.":[24]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-05T00:00:00"}