{"id":"W1973730560","doi":"10.1016/j.aml.2005.07.013","title":"Some double-series identities and associated generating-function relationships","year":2005,"lang":"en","type":"article","venue":"Applied Mathematics Letters","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Generalized hypergeometric function; Basic hypergeometric series; Hypergeometric identity; Hypergeometric function; Generating function; Series (stratigraphy); Bilateral hypergeometric series; Hypergeometric function of a matrix argument; Function (biology); Confluent hypergeometric function; Appell series; Lauricella hypergeometric series; Pure mathematics; Algebra over a field; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00163622,0.00145476,0.001128716,0.003586677,0.003173482,0.003989172,0.001768023,0.002042037,0.01122593],"category_scores_gemma":[0.003227102,0.0005728083,0.001349247,0.003582714,0.002652216,0.005171095,0.001668717,0.003379542,0.002992564],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001542466,"about_ca_system_score_gemma":0.0007770676,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000563529,"about_ca_topic_score_gemma":0.0006674248,"domain_scores_codex":[0.999509,0.0001181712,0.00003890824,0.00008436686,0.0001591352,0.00009030446],"domain_scores_gemma":[0.9990882,0.0003470065,0.0001456029,0.0001146615,0.0001774798,0.0001270322],"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":[0.000004459018,0.000009138969,0.00004345786,0.00001313514,0.000001670646,0.00007053874,0.00009193845,0.0001077294,0.0001865667,0.9962701,0.0007491032,0.002452213],"study_design_scores_gemma":[0.000003820267,0.000003317037,0.00006126388,0.000008191194,0.000004269945,0.0001368723,0.00002979874,0.001335925,0.000228372,0.9962773,0.00190326,0.00000764664],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2553801,0.004616076,0.3412291,0.004947539,0.002057275,0.0001320334,0.0006164042,0.0005846788,0.3904368],"genre_scores_gemma":[0.8479773,0.003887761,0.06272008,0.001266748,0.002403024,0.0002506211,0.0006505707,0.0004200044,0.08042386],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01122593,"threshold_uncertainty_score":0.0375545,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0494111025492326,"score_gpt":0.2595120858123733,"score_spread":0.2101009832631408,"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."}}