{"id":"W4214723443","doi":"10.29020/nybg.ejpam.v15i1.4153","title":"Definite Integrals Involving Logarithmic Powers, Binomials and Polynomials Expressed in terms of the Lerch Function","year":2022,"lang":"en","type":"article","venue":"European Journal of Pure and Applied Mathematics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Pure mathematics; Logarithm; Function (biology); Algebra over a field; Mathematical analysis","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":[0.003482917,0.0002203165,0.0006462706,0.0002343614,0.0001925534,0.00005738206,0.0003284517,0.00004151377,0.0001354706],"category_scores_gemma":[0.0004092554,0.0001482616,0.0001317609,0.0002458002,0.0001210138,0.00008401687,0.0003494641,0.000492797,0.000002382521],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003782776,"about_ca_system_score_gemma":0.00003683054,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001228184,"about_ca_topic_score_gemma":0.000002519117,"domain_scores_codex":[0.997629,0.0003403579,0.001298086,0.0001661872,0.000351621,0.0002146929],"domain_scores_gemma":[0.9975518,0.000962496,0.00103832,0.0003177439,0.00004313483,0.00008650356],"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":[0.0004919949,0.001657486,0.0008078617,0.00241266,0.0004416492,0.00005574168,0.02096881,0.0001500513,0.2043597,0.7351261,0.02066857,0.01285942],"study_design_scores_gemma":[0.005593858,0.001094192,0.001522073,0.001524462,0.0007423576,0.000703871,0.01637522,0.0003818843,0.01569749,0.9475438,0.007906685,0.0009140855],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9839448,0.0003542384,0.002080314,0.0003393533,0.0002592684,0.0004856311,0.00002986175,0.00001620662,0.01249029],"genre_scores_gemma":[0.9858359,0.0001052085,0.01349755,0.0001313493,0.0001072599,0.00001045844,8.979337e-7,0.00005024758,0.0002611],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2124177,"threshold_uncertainty_score":0.6045934,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03627595298456107,"score_gpt":0.2461048952580928,"score_spread":0.2098289422735318,"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."}}