{"id":"W2955424465","doi":"10.3390/math7070577","title":"Some Properties and Generating Functions of Generalized Harmonic Numbers","year":2019,"lang":"en","type":"article","venue":"Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Laplace transform; Mathematics; Type (biology); Harmonic; Applied mathematics; Order (exchange); Algorithm; Mathematical analysis; Physics","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":[],"consensus_categories":[],"category_scores_codex":[0.0003227888,0.0002313517,0.0005625512,0.00009327299,0.00008963629,0.00005363928,0.0001670305,0.00008827845,0.0002078694],"category_scores_gemma":[0.0004968491,0.0001866948,0.0001036555,0.0001232279,0.0001451402,0.0003075046,0.0001527721,0.0001391596,0.000107982],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000381312,"about_ca_system_score_gemma":0.00003333159,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006859881,"about_ca_topic_score_gemma":0.000005313474,"domain_scores_codex":[0.9984453,0.00003920481,0.0006662845,0.000229005,0.0003402993,0.0002798598],"domain_scores_gemma":[0.9986537,0.0003588563,0.0003080775,0.000495528,0.0001098534,0.00007395624],"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":[0.00001251493,0.0003521378,0.0001861079,0.004538803,0.0001699938,0.000002676069,0.00462215,0.00008489341,0.09020055,0.8982243,0.001412031,0.0001938737],"study_design_scores_gemma":[0.0006609848,0.00006873976,0.00000979944,0.0004057786,0.0001276377,0.00003375881,0.002467877,0.01196985,0.02369203,0.9600527,0.0001817679,0.0003290403],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9878565,0.0006155193,0.007638478,0.00008387298,0.0001767611,0.000589107,0.000009833833,0.0001506328,0.002879275],"genre_scores_gemma":[0.5838497,0.000151714,0.3744591,0.00006824991,0.0001699393,0.0001001355,0.00000463412,0.0001366986,0.04105983],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4040068,"threshold_uncertainty_score":0.7613193,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07737947560362408,"score_gpt":0.2882744919347279,"score_spread":0.2108950163311039,"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."}}