{"id":"W4294804933","doi":"10.5206/mt.v2i1.14445","title":"Difference equation satisfied by the Stieltjes transform of a sequence","year":2022,"lang":"en","type":"article","venue":"Maple Transactions","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Sequence (biology); Riemann–Stieltjes integral; Factorial; Recurrence relation; Orthogonal polynomials; Basis (linear algebra); Class (philosophy); Generating function; Orthogonality; Pure mathematics; Mathematical analysis; Integral equation; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003429242,0.0001039899,0.0001811472,0.00004612905,0.0004728822,0.00001597989,0.0001956418,0.00003002179,0.005844719],"category_scores_gemma":[0.00004056243,0.00007684044,0.0001119601,0.0002507315,0.00007446259,0.00004941724,0.00000652601,0.0002071671,0.000006398805],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004515737,"about_ca_system_score_gemma":0.00004543628,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001843041,"about_ca_topic_score_gemma":0.0000781624,"domain_scores_codex":[0.998959,0.0001104927,0.0003435235,0.0001293344,0.0003035422,0.0001541085],"domain_scores_gemma":[0.9987088,0.0008491645,0.00008742134,0.0002859696,0.00003086512,0.00003778584],"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":[0.0002994509,0.002672363,0.00009606676,0.0009438727,0.0005394959,0.00000342153,0.02481005,0.001809211,0.1167674,0.6490334,0.03131986,0.1717054],"study_design_scores_gemma":[0.001806082,0.0007621094,0.0002226813,0.00006737487,0.0006492265,0.00008500319,0.007607719,0.02260149,0.03955247,0.8842461,0.04162725,0.0007725231],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05822242,0.00006956845,0.9328349,0.002605305,0.0002040655,0.000590047,0.0005994319,0.00008664788,0.004787677],"genre_scores_gemma":[0.9925224,0.00001229824,0.001910246,0.00006717396,0.00001300866,0.000314324,0.00001285261,0.0000142816,0.00513337],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9343,"threshold_uncertainty_score":0.9950641,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1032639537311907,"score_gpt":0.307245516459297,"score_spread":0.2039815627281063,"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."}}