{"id":"W2041929385","doi":"10.1007/s11139-006-9577-0","title":"Linearization formula for the product of associated q-ultraspherical polynomials","year":2006,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"","keywords":"Linearization; Gegenbauer polynomials; Mathematics; Product (mathematics); Orthogonal polynomials; Mehler–Heine formula; Applied mathematics; Pure mathematics; Classical orthogonal polynomials; Nonlinear system; Physics; Geometry","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":[0.002210892,0.000132942,0.0002899058,0.00002949468,0.0004584622,0.00009306722,0.0003000773,0.0000602112,0.000243737],"category_scores_gemma":[0.001970692,0.00006319927,0.0002265525,0.0001735195,0.00009780948,0.0000743164,0.0000254059,0.0002201295,0.000007441909],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003918996,"about_ca_system_score_gemma":0.00006621397,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001734992,"about_ca_topic_score_gemma":0.00001227619,"domain_scores_codex":[0.9985523,0.0001509112,0.0006834574,0.00009735335,0.000261799,0.0002541519],"domain_scores_gemma":[0.9962817,0.002664904,0.0005129284,0.0002943737,0.0002049962,0.00004113568],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0005977112,0.001982949,0.001243325,0.0003301914,0.001080386,0.000003558045,0.002190761,0.00192432,0.02441343,0.44876,0.4943024,0.02317098],"study_design_scores_gemma":[0.00266321,0.0004571878,0.003348006,0.0001904732,0.001023014,0.000235839,0.0004982714,0.01218989,0.02588826,0.922468,0.0305662,0.0004716656],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4403653,0.0007402631,0.5373459,0.01174038,0.00136465,0.002423507,0.00007107522,0.0001104675,0.005838419],"genre_scores_gemma":[0.9854932,0.00001990686,0.007925478,0.00009131034,0.001562274,0.00003620977,0.000006378401,0.00003816856,0.004827084],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5451279,"threshold_uncertainty_score":0.3526167,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0456501631412661,"score_gpt":0.3080184972748041,"score_spread":0.262368334133538,"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."}}