{"id":"W3205077456","doi":"10.14232/actasm-021-465-4","title":"Orthonormal polynomial basis in local Dirichlet spaces","year":2021,"lang":"en","type":"article","venue":"Acta Scientiarum Mathematicarum","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"Agence Nationale de la Recherche","keywords":"Mathematics; Orthogonal polynomials; Discrete orthogonal polynomials; Classical orthogonal polynomials; Orthogonal basis; Pure mathematics; Dirichlet distribution; Orthonormal basis; Combinatorics; Mathematical analysis","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":[0.001659574,0.001087022,0.001402981,0.003611153,0.00211668,0.004342908,0.001980006,0.001583757,0.009871127],"category_scores_gemma":[0.003442078,0.0006257348,0.0007110179,0.002490961,0.003757171,0.00395798,0.00297049,0.003362889,0.00216959],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002020277,"about_ca_system_score_gemma":0.001039612,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001538946,"about_ca_topic_score_gemma":0.001377759,"domain_scores_codex":[0.9988231,0.0004408838,0.0000408837,0.0001929678,0.0002937034,0.0002084493],"domain_scores_gemma":[0.9985359,0.0003840877,0.0001601241,0.000162986,0.0003716142,0.0003853149],"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":[0.00001359488,0.00001155275,0.00003144579,0.00001520178,0.000002769148,0.00001748113,0.00007398071,0.0004302754,0.0003021643,0.9964077,0.0006186626,0.002075172],"study_design_scores_gemma":[0.00001107047,0.0000128709,0.0001174802,0.000009446446,0.000004890956,0.00005545777,0.00008670724,0.006695675,0.000259262,0.9904444,0.002289069,0.00001368397],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3168438,0.003979044,0.428051,0.005281392,0.00181172,0.00009677909,0.0007594565,0.0005574125,0.2426194],"genre_scores_gemma":[0.8575019,0.002463741,0.05012477,0.0006183588,0.001557997,0.0001317676,0.0005147082,0.0004191259,0.08666769],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009871127,"threshold_uncertainty_score":0.03302222,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03215861280796126,"score_gpt":0.2965944309561965,"score_spread":0.2644358181482352,"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."}}