{"id":"W2581465551","doi":"10.1002/mma.4289","title":"Reduction and transformation formulas for the Appell and related functions in two variables","year":2017,"lang":"en","type":"article","venue":"Mathematical Methods in the Applied Sciences","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Appell series; Mathematics; Hypergeometric function; Bilateral hypergeometric series; Lauricella hypergeometric series; Generalized hypergeometric function; Basic hypergeometric series; Transformation (genetics); Reduction (mathematics); Hypergeometric function of a matrix argument; Hypergeometric identity; Hypergeometric distribution; Ordinary differential equation; Pure mathematics; Function (biology); Simple (philosophy); Applied mathematics; Algebra over a field; Differential equation; Mathematical analysis; 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":[0.01198067,0.000157936,0.0003122195,0.0001062281,0.001152196,0.0003468615,0.0004310044,0.00007494529,0.00005541299],"category_scores_gemma":[0.001890532,0.00008059942,0.00004940421,0.0002199164,0.000741309,0.0002359729,0.00006853111,0.0002074277,0.000005004663],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001686634,"about_ca_system_score_gemma":0.00002163366,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001549184,"about_ca_topic_score_gemma":0.00001860692,"domain_scores_codex":[0.9984902,0.0002000449,0.0005631353,0.0002582062,0.0002100498,0.0002783509],"domain_scores_gemma":[0.9917821,0.007511968,0.000195688,0.0004505331,0.00002012409,0.00003957934],"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":[0.0000165318,0.00006902836,0.000007904441,0.0001462129,0.000009814746,1.149032e-7,0.003501078,0.00001855067,0.0007626872,0.9814219,0.00007645326,0.01396973],"study_design_scores_gemma":[0.0004757716,0.00003681709,0.00008140873,0.00006179364,0.00006001047,0.00003982967,0.00396086,0.02754897,0.0005319578,0.9667929,0.0002995911,0.0001100853],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.06314169,0.0001277344,0.8445618,0.005138574,0.0002459997,0.002628561,0.000006589819,0.00004412815,0.08410491],"genre_scores_gemma":[0.495604,0.00002624051,0.5034477,0.00005969121,0.00005726028,0.0005329217,6.404858e-7,0.00001336265,0.0002582568],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4324623,"threshold_uncertainty_score":0.8861877,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1367325340463885,"score_gpt":0.4526132346417133,"score_spread":0.3158807005953247,"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."}}