{"id":"W2045104701","doi":"10.4153/cmb-2008-055-0","title":"Expansion of the Riemann Ξ Function in Meixner–Pollaczek Polynomials","year":2008,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada; McMaster University","keywords":"Mathematics; Asymptotic expansion; Pure mathematics; Riemann hypothesis; Function (biology); Edgeworth series; Recurrence relation; Orthogonal polynomials; Mathematical analysis; Applied mathematics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.000564062,0.0002655945,0.0005981639,0.0002268185,0.0001889312,0.00001816505,0.0004375195,0.0001841792,0.005572739],"category_scores_gemma":[0.003306299,0.0001974264,0.0001986646,0.0003799693,0.0004353144,0.00007202626,0.00009834618,0.0002947004,0.001329095],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002482622,"about_ca_system_score_gemma":0.0003033636,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007277923,"about_ca_topic_score_gemma":0.001994863,"domain_scores_codex":[0.9976261,0.0001511806,0.0008890165,0.0002947391,0.0004756927,0.0005632238],"domain_scores_gemma":[0.997662,0.0009494032,0.0002215838,0.0007460411,0.0001055327,0.0003154174],"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":[0.00003516533,0.0001975912,0.000354459,0.000696312,0.00004328505,0.0000650959,0.001795049,0.00001547299,0.0008336257,0.9553225,0.04048855,0.0001528992],"study_design_scores_gemma":[0.00047124,0.00004155546,0.0008379848,0.0003612712,0.00004164645,0.00007723976,0.0004738045,0.00007498388,0.001773694,0.991535,0.00404696,0.0002646297],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9089029,0.0001812165,0.00511731,0.004292937,0.0003286732,0.00133129,0.00003676548,0.0001116315,0.07969721],"genre_scores_gemma":[0.9807644,0.00001395552,0.00804709,0.0003263541,0.00007498519,0.00007318724,0.00000198539,0.00006551066,0.01063251],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07186145,"threshold_uncertainty_score":0.9994485,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03745156650565997,"score_gpt":0.2566529487543158,"score_spread":0.2192013822486558,"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."}}