{"id":"W4392040436","doi":"10.21203/rs.3.rs-3969711/v1","title":"Berndt-Type Integrals of Order Three and Series Associated with Jacobi Elliptic Functions","year":2024,"lang":"en","type":"preprint","venue":"Research Square","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Bishop's University","funders":"","keywords":"Mathematics; Trigonometric functions; Jacobi elliptic functions; Fourier series; Type (biology); Elliptic function; Elliptic integral; Hyperbolic function; Series (stratigraphy); Trigonometry; Order (exchange); Function (biology); Gamma function; Applied mathematics; Theta function; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001263903,0.0003362591,0.0007244899,0.0004367555,0.0001585713,0.0002136586,0.0003298416,0.0003501954,0.0003979146],"category_scores_gemma":[0.006748534,0.0002507359,0.0001021993,0.0008169694,0.0007974221,0.0001328349,0.001780672,0.001955559,0.0000822725],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002184425,"about_ca_system_score_gemma":0.000416846,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009323946,"about_ca_topic_score_gemma":0.001455035,"domain_scores_codex":[0.9970106,0.0002221025,0.0005101723,0.0005311897,0.001196443,0.0005294568],"domain_scores_gemma":[0.9948615,0.002172247,0.000170571,0.0007665385,0.001888887,0.000140291],"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":[0.0003361278,0.0008998639,0.001744126,0.04321694,0.002290981,0.000173065,0.005471019,0.000173352,0.0004646036,0.9265569,0.01794292,0.0007301028],"study_design_scores_gemma":[0.0001669461,0.0003556365,0.0002532461,0.00601604,0.0001640471,0.000009767572,0.002328385,0.0003413273,0.0003367156,0.9895854,0.000186296,0.0002562055],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9618729,0.005042172,0.003910235,0.001214765,0.0004900253,0.003373961,0.0005543712,0.0006080191,0.0229335],"genre_scores_gemma":[0.8751997,0.0008478619,0.01789189,0.000007508581,0.0002307791,0.000567036,0.000159798,0.000349555,0.1047458],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08667322,"threshold_uncertainty_score":0.9999945,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1431153567734955,"score_gpt":0.4310248505963381,"score_spread":0.2879094938228426,"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."}}