{"id":"W4410535371","doi":"10.1371/journal.pone.0320045","title":"Extended Levett trigonometric series","year":2025,"lang":"en","type":"article","venue":"PLoS ONE","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Trigonometric series; Series (stratigraphy); Trigonometric functions; Trigonometric substitution; Trigonometric integral; Integration using Euler's formula; Mathematics; Trigonometry; Pythagorean trigonometric identity; Inverse trigonometric functions; Differentiation of trigonometric functions; Riemann zeta function; Trigonometric polynomial; Pure mathematics; Mathematical analysis; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005459849,0.0006358378,0.000675153,0.002120546,0.0009612275,0.002252782,0.0006989314,0.0005803182,0.01100526],"category_scores_gemma":[0.001890392,0.0001416436,0.000884659,0.00130792,0.001286556,0.002430023,0.001066667,0.001711669,0.002221203],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001296264,"about_ca_system_score_gemma":0.0006269771,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000473312,"about_ca_topic_score_gemma":0.0005458473,"domain_scores_codex":[0.9996096,0.00008477388,0.00002157276,0.00007096341,0.0001536932,0.00005936593],"domain_scores_gemma":[0.999522,0.0001155334,0.00004927061,0.00009807204,0.0001470869,0.00006803261],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003215738,0.00001954851,0.0001568605,0.00005231269,0.000006320839,0.000291403,0.0001365315,0.002176808,0.001827386,0.9781188,0.00160465,0.01557723],"study_design_scores_gemma":[0.00001478365,0.00004432873,0.0003478254,0.00006022121,0.00001496953,0.0005024045,0.00008019879,0.02868842,0.002044821,0.9396099,0.02856615,0.00002603853],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.1858378,0.003939406,0.2971818,0.001870796,0.002456103,0.00009476144,0.0003138277,0.0009087812,0.5073967],"genre_scores_gemma":[0.8376483,0.002305689,0.05417142,0.0005356653,0.001001254,0.00009863622,0.0002826262,0.0002851595,0.1036713],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.01100526,"threshold_uncertainty_score":0.03681624,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1257214919171939,"score_gpt":0.3179228834105794,"score_spread":0.1922013914933856,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}