{"id":"W1977710459","doi":"10.1016/j.camwa.2011.09.010","title":"Some series identities involving the generalized Apostol type and related polynomials","year":2011,"lang":"en","type":"article","venue":"Computers & Mathematics with Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":57,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Wilson polynomials; Difference polynomials; Classical orthogonal polynomials; Discrete orthogonal polynomials; Macdonald polynomials; Hahn polynomials; Orthogonal polynomials; Koornwinder polynomials; Pure mathematics; Gegenbauer polynomials; Combinatorics","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":[0.0003184601,0.0003077766,0.0004526236,0.0001113557,0.0004409222,0.0001527898,0.0004908824,0.00009097067,0.0000662127],"category_scores_gemma":[0.0001616944,0.000211098,0.00006194103,0.0003069702,0.000565302,0.0004948095,0.0002583675,0.0001969868,0.00006613809],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000042185,"about_ca_system_score_gemma":0.00005216401,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009375603,"about_ca_topic_score_gemma":0.00001127339,"domain_scores_codex":[0.9983903,0.00005443737,0.0006269414,0.0003180545,0.0002813766,0.0003289574],"domain_scores_gemma":[0.9977679,0.0006554128,0.000388042,0.0008529747,0.0002206806,0.0001149779],"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":[0.00001021908,0.0001277813,0.00001615852,0.0003365718,0.0001265085,0.000003772945,0.006638729,0.000004129809,0.0002437489,0.9911626,0.001213179,0.0001166028],"study_design_scores_gemma":[0.000312864,0.00005865274,0.00003614176,0.0001368125,0.0001760064,0.0002016298,0.001304214,0.0006775236,0.0008846468,0.9955487,0.0003789469,0.0002838765],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.2814831,0.006953125,0.661197,0.002192641,0.0009759555,0.01106583,0.00007351497,0.003070142,0.03298865],"genre_scores_gemma":[0.05525695,0.0007091232,0.9317418,0.0002052092,0.0002329112,0.001049915,0.0000178329,0.0001969867,0.01058929],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2705448,"threshold_uncertainty_score":0.8608328,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04949446309089626,"score_gpt":0.2791595427004343,"score_spread":0.2296650796095381,"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."}}