{"id":"W3048128516","doi":"10.48550/arxiv.1809.04636","title":"Connection Coefficients for Higher-order Bernoulli and Euler\\n Polynomials: A Random Walk Approach","year":2018,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"","keywords":"Bernoulli's principle; Mathematics; Connection (principal bundle); Random walk; Euler's formula; Order (exchange); Bernoulli process; Brownian motion; Bessel process; Bernoulli polynomials; Mathematical analysis; Orthogonal polynomials; Pure mathematics; Discrete orthogonal polynomials; Classical orthogonal polynomials; Gegenbauer polynomials; Physics; Geometry; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001828811,0.0008304964,0.0008523145,0.004009238,0.001115,0.001901366,0.001626145,0.001417825,0.006700166],"category_scores_gemma":[0.009200446,0.000570618,0.0009435334,0.001624952,0.002693208,0.003772393,0.002271162,0.002888018,0.0009465733],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001435741,"about_ca_system_score_gemma":0.001075514,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001539987,"about_ca_topic_score_gemma":0.001907975,"domain_scores_codex":[0.9993569,0.000214192,0.00002515186,0.00008766213,0.000202257,0.0001138331],"domain_scores_gemma":[0.9967719,0.001607447,0.0004461911,0.0002453502,0.0004831047,0.000446018],"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":[0.000006026338,0.00001264509,0.0001972422,0.00002023247,0.000003655131,0.00007457034,0.00006333912,0.003431006,0.0006743672,0.9929338,0.0003860209,0.002197119],"study_design_scores_gemma":[0.00001131934,0.00001256924,0.000397713,0.00002881168,0.000006604868,0.0001805658,0.00004711955,0.1042465,0.0005502483,0.8925354,0.001952628,0.00003053871],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.3827623,0.002464811,0.5333043,0.002882486,0.0007139119,0.0001223653,0.0002137285,0.0002664914,0.07726962],"genre_scores_gemma":[0.9175849,0.001907463,0.05768714,0.0003876161,0.0006113176,0.0001329947,0.0001473851,0.0002384264,0.02130277],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.006700166,"threshold_uncertainty_score":0.02241427,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1157427882986082,"score_gpt":0.2411576889787984,"score_spread":0.1254149006801902,"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."}}