{"id":"W4319441357","doi":"10.20944/preprints202302.0082.v1","title":"A Generalized Series Expansion of the Arctangent Function Based on the Enhanced Midpoint Integration","year":2023,"lang":"en","type":"preprint","venue":"Preprints.org","topic":"Digital Filter Design and Implementation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Thoth Technology (Canada); York University","funders":"National Research Council Canada; York University","keywords":"Midpoint; Inverse trigonometric functions; Series (stratigraphy); Convergence (economics); Mathematics; Function (biology); Series expansion; Taylor series; Midpoint method; Simple (philosophy); Applied mathematics; Computation; Function series; Sine; Numerical integration; Trigonometric functions; Mathematical analysis; Power series; Algorithm; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0004841923,0.0005509573,0.0005425546,0.0005949033,0.0002179333,0.0006017089,0.0009169258,0.0004630858,0.003802214],"category_scores_gemma":[0.001061186,0.0001806097,0.0004864508,0.0006426304,0.0005109422,0.0009875275,0.0005164074,0.001006079,0.00134249],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003845462,"about_ca_system_score_gemma":0.0003660507,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002994647,"about_ca_topic_score_gemma":0.0005019291,"domain_scores_codex":[0.9997495,0.00005326944,0.00001088489,0.00003278275,0.0001362456,0.00001736601],"domain_scores_gemma":[0.999793,0.00006464511,0.00001563123,0.00004448331,0.00006962214,0.00001264314],"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":[0.00009444678,0.00007019913,0.0003957461,0.0003666336,0.00004842384,0.0003570254,0.0002162544,0.1458997,0.07693344,0.5455641,0.003214499,0.2268395],"study_design_scores_gemma":[0.00001534291,0.00008412737,0.0001526848,0.00003360824,0.00001985524,0.0003267994,0.00002397948,0.9062389,0.01934359,0.05845057,0.01528863,0.00002193865],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.005213614,0.0002752115,0.9897406,0.00004657819,0.00009537512,0.00001522406,0.00001507295,0.0001321714,0.004466107],"genre_scores_gemma":[0.2520626,0.001240366,0.7363844,0.0001534435,0.0002393981,0.00009862897,0.00009386522,0.000343871,0.009383506],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.003802214,"threshold_uncertainty_score":0.01271963,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1876998488798979,"score_gpt":0.3336665869498514,"score_spread":0.1459667380699534,"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."}}