{"id":"W3105552015","doi":"","title":"Integral and Series Representations of Riemann’s Zeta Function and Dirichlet’s Eta Function and a Medley of Related Results","year":2016,"lang":"en","type":"article","venue":"","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":34,"is_retracted":false,"has_abstract":true,"ca_institutions":"Ducks Unlimited Canada","funders":"","keywords":"Riemann zeta function; Mathematics; Dirichlet series; Riemann hypothesis; Series (stratigraphy); Arithmetic zeta function; Function (biology); Dirichlet eta function; Dirichlet L-function; Particular values of Riemann zeta function; General Dirichlet series; Pure mathematics; Mathematical analysis; Explicit formulae; Dirichlet distribution; Prime zeta function; Calculus (dental)","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":[0.0002877274,0.0001253022,0.0002934686,0.0001022487,0.00005390738,0.00001604845,0.00003837222,0.00008234978,0.00005707735],"category_scores_gemma":[0.001678793,0.00008028779,0.00003068843,0.0001113871,0.0003879511,0.000519839,0.00009860386,0.00006369551,0.000001778802],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001219945,"about_ca_system_score_gemma":0.00001120229,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003390856,"about_ca_topic_score_gemma":0.00010608,"domain_scores_codex":[0.9989006,0.00005192602,0.0005401813,0.0002263547,0.0001690389,0.0001118989],"domain_scores_gemma":[0.998481,0.0008083841,0.0002570509,0.0002509751,0.0001476623,0.00005490646],"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":[0.0005426716,0.0001150472,0.002054753,0.0006235529,0.0001778286,0.000001082184,0.001735308,6.578957e-7,0.02177977,0.9700279,0.001630036,0.001311412],"study_design_scores_gemma":[0.001141438,0.0002341045,0.009583461,0.0002156724,0.0001601218,0.00001864822,0.001970124,0.00004830332,0.003414092,0.9830413,0.00006723728,0.0001055092],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9507406,0.0003242184,0.03458177,0.001409849,0.0001324519,0.0004570266,0.0000510653,0.0001243702,0.01217868],"genre_scores_gemma":[0.9759407,0.0002070706,0.007164011,0.000007828544,0.00001249519,0.00001329852,0.000003687468,0.0000168585,0.01663405],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02741776,"threshold_uncertainty_score":0.3274041,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03329707386127455,"score_gpt":0.2983636278361627,"score_spread":0.2650665539748881,"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."}}