{"id":"W3085237204","doi":"10.1186/s13662-020-02963-9","title":"Generating functions for some families of the generalized Al-Salam–Carlitz q-polynomials","year":2020,"lang":"en","type":"article","venue":"Advances in Difference Equations","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Homogeneous; Type (biology); Order (exchange); Combinatorics; Algebra over a field; Pure mathematics; Discrete mathematics","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":[0.0002605978,0.0001841012,0.0004158115,0.00006726706,0.0002413451,0.00003154596,0.0002992826,0.00005793424,0.0001202732],"category_scores_gemma":[0.004309703,0.0001307814,0.0001828347,0.0003580583,0.0001262114,0.0002456913,0.00008274914,0.0001361759,0.000008055756],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003420357,"about_ca_system_score_gemma":0.00008301632,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001424102,"about_ca_topic_score_gemma":0.00009609757,"domain_scores_codex":[0.9983834,0.0001226155,0.0007618899,0.0002661224,0.0002143155,0.0002516241],"domain_scores_gemma":[0.9964957,0.002662721,0.0002966487,0.0003807974,0.00009430137,0.00006983944],"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":[0.00004078427,0.0002327063,0.001136036,0.0003291014,0.00005300497,2.35807e-7,0.0018736,0.003881207,0.02807157,0.9499071,0.003073095,0.01140154],"study_design_scores_gemma":[0.002353636,0.0002745844,0.0005418947,0.0003163387,0.0002361233,0.000002096034,0.001865016,0.1443541,0.0171856,0.8095737,0.0225656,0.0007313634],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4380036,0.001483592,0.549581,0.006328868,0.0009680025,0.001807245,0.0003333727,0.000121601,0.001372703],"genre_scores_gemma":[0.9575922,0.0002846984,0.03888202,0.001159202,0.0003478747,0.0007173885,0.00002366057,0.00003750293,0.0009554076],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5195886,"threshold_uncertainty_score":0.5333112,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07435807561391443,"score_gpt":0.3353025468680516,"score_spread":0.2609444712541371,"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."}}