{"id":"W2398255516","doi":"","title":"HIGH ORDER DERIVATIVES AND TWO q-IDENTITIES RELATED TO PRODINGER'S FORMULA","year":2013,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Order (exchange); Pure mathematics; Business","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":[],"consensus_categories":[],"category_scores_codex":[0.0001926416,0.000238433,0.0003775909,0.0001239683,0.000168462,0.0001795868,0.0002110319,0.00007492399,0.0003444247],"category_scores_gemma":[0.001328994,0.0002156469,0.00004204366,0.000296141,0.0001349725,0.0007238505,0.0002616819,0.0001654779,0.0002986542],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005713338,"about_ca_system_score_gemma":0.00001965381,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004514527,"about_ca_topic_score_gemma":0.000006563031,"domain_scores_codex":[0.9985726,0.00004928921,0.0004207153,0.0002972862,0.0002920584,0.0003680801],"domain_scores_gemma":[0.9985579,0.0005120408,0.0001288839,0.0003750563,0.0002734283,0.0001527316],"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":[0.000002790216,0.00007736192,0.0002275889,0.0001204797,0.00004745499,0.000003795021,0.001584677,0.000001988213,0.0009524974,0.9928461,0.003984945,0.000150326],"study_design_scores_gemma":[0.0006566698,0.00007279465,0.0004933592,0.0001049323,0.00002729065,0.000009829439,0.0006131062,0.00005566483,0.003895155,0.9937038,0.0000976531,0.0002696918],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9932688,0.000071774,0.0003708298,0.0004883739,0.0005586368,0.0008221916,0.000002544148,0.0002557767,0.00416101],"genre_scores_gemma":[0.9592773,0.00001529622,0.02864931,0.00007194068,0.000007676329,0.0002133812,0.000002716212,0.00006099039,0.01170144],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03399161,"threshold_uncertainty_score":0.8793826,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01849092649665718,"score_gpt":0.294740387397923,"score_spread":0.2762494609012658,"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."}}