{"id":"W4400154213","doi":"10.69829/apna-024-0101-ta01","title":"Some generating functions of the Bessel and related orthogonal polynomials","year":2024,"lang":"en","type":"article","venue":"Applicable Nonlinear Analysis","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Orthogonal polynomials; Bessel function; Bessel polynomials; Mathematics; Gegenbauer polynomials; Discrete orthogonal polynomials; Classical orthogonal polynomials; Pure mathematics; Wilson polynomials; Bessel process; Jacobi polynomials; Algebra over a field; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000576722,0.0001558892,0.0004453207,0.0001881968,0.0002021845,0.00007486468,0.000135601,0.0001121508,0.000575673],"category_scores_gemma":[0.0001509496,0.0001011214,0.0004020506,0.001423751,0.0000984767,0.00008462706,0.00009976592,0.0001881462,0.00003276268],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001894453,"about_ca_system_score_gemma":0.00005667929,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004752365,"about_ca_topic_score_gemma":0.00004389307,"domain_scores_codex":[0.998643,0.0000681136,0.0005918124,0.000292492,0.0002165756,0.000187991],"domain_scores_gemma":[0.9985576,0.0007395905,0.0001162601,0.0004602612,0.00005497225,0.00007134287],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003526907,0.0007657327,0.00356055,0.001428356,0.01410346,0.00001044807,0.0009988727,0.002371653,0.06686767,0.8744076,0.0233272,0.0121232],"study_design_scores_gemma":[0.0006432441,0.00009663183,0.0005921492,0.0002271408,0.01672954,0.00006146961,0.0005539507,0.6639149,0.01490795,0.2497213,0.05166807,0.0008835718],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9730197,0.0021525,0.01806151,0.001112417,0.0002812627,0.0004658152,0.0002888211,0.0001857139,0.004432314],"genre_scores_gemma":[0.9338067,0.0001491989,0.0286581,0.0001555384,0.0007705248,0.0001248674,0.00005394459,0.0000746966,0.03620639],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6615433,"threshold_uncertainty_score":0.6303215,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02148668991862947,"score_gpt":0.289457949513332,"score_spread":0.2679712595947025,"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."}}