{"id":"W4221039451","doi":"10.1155/2022/7044988","title":"A Double Integral Containing the Fresnel Integral Function <i>S</i>(<i>x</i>): Derivation and Computation","year":2022,"lang":"en","type":"article","venue":"Journal of Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Fresnel integral; Physics; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001672801,0.0001858832,0.0004248754,0.0001612579,0.0004040543,0.0001115293,0.000268089,0.000043403,0.00009353294],"category_scores_gemma":[0.0006759097,0.0001270722,0.0001424415,0.0002327742,0.0001186911,0.0003708474,0.0001987381,0.0006159498,0.000002845178],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001461031,"about_ca_system_score_gemma":0.00006270683,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005796403,"about_ca_topic_score_gemma":0.000009112519,"domain_scores_codex":[0.9979047,0.0001184836,0.0009541876,0.0001156338,0.0007029936,0.0002040523],"domain_scores_gemma":[0.9970167,0.001316286,0.001134895,0.0001860705,0.0002782023,0.00006783316],"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":[0.0003994543,0.0007027691,0.0001641496,0.0005888717,0.0002984831,0.0000317287,0.01879511,0.00117923,0.001584339,0.9661294,0.007879315,0.002247208],"study_design_scores_gemma":[0.00130179,0.0004410937,0.00004264631,0.0001230152,0.0001972436,0.0006393109,0.02617477,0.006103621,0.0002671886,0.9639219,0.0006397101,0.0001477389],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.662912,0.0002781916,0.3335132,0.0009021529,0.0005149387,0.0004186341,0.000005890854,0.00006010705,0.001394928],"genre_scores_gemma":[0.9099863,0.00002031092,0.08901522,0.0001777249,0.0001701951,0.00003239177,0.000002818046,0.00004878999,0.0005463135],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2470742,"threshold_uncertainty_score":0.5181854,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06675358945227225,"score_gpt":0.3267937332569067,"score_spread":0.2600401438046345,"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."}}