{"id":"W4214583516","doi":"10.29020/nybg.ejpam.v15i1.4181","title":"Extended Apelblat Integrals for Fractional Calculus","year":2022,"lang":"en","type":"article","venue":"European Journal of Pure and Applied Mathematics","topic":"Fractional Differential Equations Solutions","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; Logarithm; Fractional calculus; Gamma function; Pure mathematics; Polylogarithm; Exponential function; Polynomial; Riemann zeta function; Calculus (dental); Arithmetic zeta function; Mathematical analysis; Prime zeta function","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":[0.00120445,0.0001464986,0.000283523,0.000157604,0.0004104483,0.0000461888,0.0002081262,0.00001885331,0.0003193283],"category_scores_gemma":[0.0003161687,0.0001270822,0.000157362,0.0001297626,0.00004835295,0.00008516118,0.0001033171,0.0003719242,0.00001039043],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007136137,"about_ca_system_score_gemma":0.00005700623,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":1.575723e-7,"about_ca_topic_score_gemma":5.609158e-7,"domain_scores_codex":[0.9985542,0.00008876863,0.0006577712,0.0001199372,0.000416228,0.0001630653],"domain_scores_gemma":[0.9982825,0.0006829949,0.0006394701,0.0001514788,0.0001491099,0.00009443599],"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":[0.00007780155,0.0006800213,0.000001411414,0.0001009774,0.0001802913,0.00001261288,0.00115584,0.0002053435,0.003571355,0.9665558,0.02099886,0.006459732],"study_design_scores_gemma":[0.00232957,0.0005132078,0.0002089537,0.00008343831,0.0004600176,0.000857336,0.006060448,0.003410965,0.0007468329,0.9493088,0.03561039,0.0004100623],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08067494,0.0001779696,0.9015844,0.000974144,0.0005063111,0.00054711,0.00008171344,0.00005372303,0.01539964],"genre_scores_gemma":[0.802799,0.00001912148,0.1955693,0.0001530016,0.0003970709,0.0000338237,0.00001138384,0.00006750324,0.0009497698],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7221241,"threshold_uncertainty_score":0.518226,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05732053216812179,"score_gpt":0.3034054223715764,"score_spread":0.2460848902034546,"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."}}