{"id":"W2107320948","doi":"10.1016/j.jat.2009.09.008","title":"Cauchy biorthogonal polynomials","year":2009,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":68,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Saskatchewan; Université de Montréal; Concordia University","funders":"","keywords":"Mathematics; Biorthogonal system; Hermite polynomials; Orthogonal polynomials; Jacobi polynomials; Positive-definite matrix; Classical orthogonal polynomials; Peakon; Kernel (algebra); Discrete orthogonal polynomials; Pure mathematics; Cauchy distribution; Wilson polynomials; Hermitian matrix; Gegenbauer polynomials; Inverse; Difference polynomials; Laguerre polynomials; Random matrix; Mathematical analysis; Eigenvalues and eigenvectors","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":[0.0005291958,0.0000725603,0.0001519975,0.00007530541,0.00005372475,0.00003551393,0.0001019987,0.00002251314,0.0003793716],"category_scores_gemma":[0.00001119028,0.00005607112,0.0001458701,0.0000700061,0.00002237789,0.0001768155,0.000006809578,0.0001273866,0.0000168762],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001155204,"about_ca_system_score_gemma":0.00006087449,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":9.480895e-7,"about_ca_topic_score_gemma":3.371781e-8,"domain_scores_codex":[0.9993113,0.00006786249,0.0003273313,0.00005335024,0.0001332404,0.0001068861],"domain_scores_gemma":[0.9993942,0.00005053629,0.0003100228,0.00008596772,0.00009089965,0.00006834237],"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":[0.000124513,0.0003084544,0.001067813,0.00000477442,0.00008740626,0.000003714686,0.0005519624,0.0001141891,0.007953386,0.8684371,0.001977504,0.1193692],"study_design_scores_gemma":[0.001203335,0.0002867437,0.009216145,0.00005125731,0.00007540431,0.00003085361,0.001015969,0.0005313994,0.01712614,0.959886,0.01033754,0.0002392229],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8668722,0.000157809,0.09438989,0.001255565,0.0003582556,0.0001197919,0.00002471599,0.00001312979,0.03680866],"genre_scores_gemma":[0.993463,0.000001939324,0.004958618,0.0001491966,0.001027664,3.274168e-7,0.000005339652,0.000005233638,0.0003886599],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1265908,"threshold_uncertainty_score":0.4153853,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007001931759014619,"score_gpt":0.2572374944246489,"score_spread":0.2502355626656342,"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."}}