{"id":"W1562878716","doi":"10.1007/s10476-009-0205-2","title":"Double trigonometric series with positive coefficients","year":2009,"lang":"en","type":"article","venue":"Analysis Mathematica","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"St. Francis Xavier University","funders":"","keywords":"Sine; Trigonometric series; Series (stratigraphy); Trigonometric functions; Mathematics; Trigonometric integral; Differentiation of trigonometric functions; Pythagorean trigonometric identity; Trigonometry; Trigonometric substitution; Mathematical analysis; Inverse trigonometric functions; Pure mathematics; Trigonometric polynomial; Geometry; Polynomial","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004342241,0.0003823112,0.001075118,0.0009944035,0.000214848,0.0001712798,0.0004063682,0.00009255775,0.0005743277],"category_scores_gemma":[0.0003682651,0.0002787358,0.0003698835,0.004160277,0.0001588446,0.0004871006,0.00005929245,0.0001736332,0.0001931215],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009574838,"about_ca_system_score_gemma":0.00003289077,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004493379,"about_ca_topic_score_gemma":0.00001607196,"domain_scores_codex":[0.9975225,0.00005243235,0.0007138232,0.0004663405,0.0007233,0.0005215561],"domain_scores_gemma":[0.9976816,0.0006320138,0.0003733414,0.0008729451,0.0002564404,0.0001836233],"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":[0.0002014502,0.001394267,0.000107392,0.000195928,0.002240537,0.00005208951,0.001840623,0.0001733807,0.0001584072,0.9925123,0.0007426416,0.0003809542],"study_design_scores_gemma":[0.00106222,0.0003678471,0.0004086955,0.000104023,0.004010697,0.0000429574,0.0008498367,0.0008561842,0.003996481,0.9876434,0.00009322692,0.0005644929],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2420575,0.000160852,0.6141672,0.0009787274,0.00004890635,0.001358232,0.0000330488,0.0007581515,0.1404374],"genre_scores_gemma":[0.8802541,0.00001096522,0.1024179,0.00008995854,0.00004075044,0.00004899256,0.00001963465,0.00004602386,0.01707169],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6381966,"threshold_uncertainty_score":0.9999665,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02912155427554964,"score_gpt":0.3143471150187003,"score_spread":0.2852255607431506,"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."}}