{"id":"W3142790969","doi":"10.1016/j.jmaa.2021.125179","title":"Harmonic sums from the Kummer theorem","year":2021,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Binomial coefficient; Harmonic number; Series (stratigraphy); Binomial theorem; Harmonic; Variety (cybernetics); Power series; Integer (computer science); Pure mathematics; Divergent series; Mathematical analysis; Discrete mathematics; Summation by parts; Statistics","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006242243,0.0001492275,0.0006038949,0.00007498966,0.0001738382,0.0001299849,0.0002934577,0.00006028913,0.0009140579],"category_scores_gemma":[0.0008500367,0.0000856297,0.000445303,0.0006817627,0.0001898485,0.000128302,0.0001113462,0.0002518081,0.00003178305],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002331905,"about_ca_system_score_gemma":0.00004229197,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003274171,"about_ca_topic_score_gemma":0.00001993931,"domain_scores_codex":[0.9983007,0.0001030573,0.0008403901,0.0001686711,0.0004204008,0.0001667801],"domain_scores_gemma":[0.9950423,0.003524827,0.0004683078,0.0004908436,0.0003457241,0.0001279462],"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":[0.000004315177,0.0003310124,0.0002193296,0.00005415356,0.0013337,0.00000857348,0.0003479827,0.000006690138,0.0006063029,0.9947082,0.001119842,0.00125986],"study_design_scores_gemma":[0.0001582143,0.000009332874,0.0004094434,0.00004579862,0.002720672,0.00004091813,0.001064135,0.0003978295,0.001758615,0.9913169,0.001976909,0.0001012374],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.076427,0.001457912,0.9149481,0.003782643,0.00002010487,0.0001830087,0.00003230702,0.00002382193,0.003125095],"genre_scores_gemma":[0.8252172,0.0007849215,0.1698004,0.0004271716,0.0005458261,0.00008359042,0.00001357301,0.00004812373,0.003079188],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7487902,"threshold_uncertainty_score":0.9999992,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03747334065102707,"score_gpt":0.3248924895625711,"score_spread":0.287419148911544,"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."}}