{"id":"W3192703224","doi":"10.1155/2021/8814756","title":"The Mellin Transform of Logarithmic and Rational Quotient Function in terms of the Lerch Function","year":2021,"lang":"en","type":"article","venue":"Journal of Mathematics","topic":"Differential Equations and Boundary Problems","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; Quotient; Function (biology); Mellin transform; Pure mathematics; Logarithmic derivative; Algebra over a field; Mathematical analysis; Laplace transform","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":[0.0009043611,0.00007982986,0.000235763,0.00006138044,0.0000869322,0.00003346421,0.0001082517,0.00005415211,0.0000347437],"category_scores_gemma":[0.0001818191,0.00004260274,0.0001251737,0.0001687555,0.00009053988,0.0001065472,0.00002444956,0.0001808256,3.836919e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003026887,"about_ca_system_score_gemma":0.0001097498,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002773027,"about_ca_topic_score_gemma":0.0001208918,"domain_scores_codex":[0.9985265,0.00007241993,0.0008566055,0.00005446215,0.0004067816,0.00008326876],"domain_scores_gemma":[0.998532,0.0004667563,0.0005989823,0.0001504837,0.0002308828,0.0000208876],"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":[0.0002309069,0.003236794,0.002684575,0.002360122,0.0006225816,0.000007316216,0.009685698,0.000675668,0.03987999,0.9018884,0.001105039,0.03762291],"study_design_scores_gemma":[0.0009368453,0.0002525206,0.002360603,0.0004769416,0.0002053729,0.00009915636,0.002415527,0.003201588,0.007206248,0.9822288,0.000541498,0.00007488503],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9504995,0.0001990676,0.04707005,0.0006684014,0.0003847688,0.0002192965,0.000005111386,0.000002743885,0.000951069],"genre_scores_gemma":[0.9954403,0.0001421834,0.004019507,0.00001164196,0.00004185864,0.000002776955,8.897569e-7,0.000009224845,0.0003316299],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08034042,"threshold_uncertainty_score":0.1737289,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03722147091147491,"score_gpt":0.2684549707829179,"score_spread":0.231233499871443,"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."}}