{"id":"W2027525228","doi":"10.1016/j.jat.2011.06.002","title":"On the convergence of expansions in polyharmonic eigenfunctions","year":2011,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematics; Eigenfunction; Convergence (economics); Asymptotic expansion; Mathematical analysis; Eigenvalues and eigenvectors; Fourier series; Rate of convergence; Applied mathematics; Computation; Key (lock)","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":[0.01122891,0.002134444,0.001987136,0.004621034,0.001736235,0.003956176,0.002992654,0.002327385,0.007141521],"category_scores_gemma":[0.03878941,0.0008529482,0.00150372,0.001988736,0.007220195,0.008565264,0.005758933,0.007173471,0.001018315],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001911586,"about_ca_system_score_gemma":0.001101926,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001819823,"about_ca_topic_score_gemma":0.001460537,"domain_scores_codex":[0.9968128,0.001659856,0.0001467906,0.0002778937,0.0007564487,0.0003462099],"domain_scores_gemma":[0.9677629,0.02447209,0.001039711,0.001267903,0.003807701,0.001649747],"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":[0.0001232745,0.0000621773,0.0005247894,0.0001257476,0.00003282137,0.0001739474,0.0003958429,0.01073142,0.001483935,0.9769316,0.002040317,0.007374083],"study_design_scores_gemma":[0.00003083231,0.00005258892,0.0005454651,0.0001002234,0.00002892541,0.0001634085,0.0001824763,0.1957075,0.0007890434,0.7999919,0.002369429,0.00003833851],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1846483,0.006287913,0.7156657,0.005896271,0.001651116,0.000120049,0.0002690197,0.0003597915,0.08510193],"genre_scores_gemma":[0.8234994,0.007884338,0.1139636,0.001962981,0.002363541,0.0003495347,0.0006487523,0.0009338871,0.04839397],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01122891,"threshold_uncertainty_score":0.05938482,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1099218744929753,"score_gpt":0.297663090976035,"score_spread":0.1877412164830597,"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."}}