{"id":"W2963710387","doi":"10.1016/j.jmaa.2015.11.006","title":"General convolution identities for Bernoulli and Euler polynomials","year":2015,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Convolution (computer science); Bernoulli's principle; Mathematics; Euler's formula; Bernoulli polynomials; Bernoulli process; Pure mathematics; Identity (music); Bernoulli number; Computation; Algebra over a field; Discrete mathematics; Orthogonal polynomials; Mathematical analysis; Difference polynomials; Computer science; Algorithm; Physics; Artificial intelligence","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002925319,0.001284257,0.001309064,0.002787477,0.00204274,0.004210321,0.001354209,0.002183625,0.007366823],"category_scores_gemma":[0.007063277,0.0007072112,0.0013624,0.002785013,0.003489153,0.0088505,0.003107219,0.003534848,0.001215339],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002405258,"about_ca_system_score_gemma":0.001662248,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002143737,"about_ca_topic_score_gemma":0.001919058,"domain_scores_codex":[0.999027,0.0002511402,0.00007534623,0.000157521,0.0003393766,0.0001495643],"domain_scores_gemma":[0.9979212,0.0008355976,0.0002361305,0.0002368418,0.000479744,0.000290461],"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":[0.000003900625,0.000004860502,0.00005727883,0.00001127363,0.000002041774,0.00002755512,0.00006105515,0.0002502483,0.0001529604,0.9974195,0.0005706362,0.001438634],"study_design_scores_gemma":[0.000002628032,0.000002582436,0.00007100468,0.000007641887,0.000002839637,0.00006981019,0.00001812047,0.002991067,0.00007538555,0.9944975,0.002254239,0.00000715262],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1284194,0.008737753,0.6308555,0.006612387,0.002628282,0.00007516189,0.0004827072,0.0003121574,0.2218767],"genre_scores_gemma":[0.7814843,0.008095909,0.107234,0.002331998,0.003796965,0.0001650176,0.0005753305,0.0003247721,0.09599171],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007366823,"threshold_uncertainty_score":0.02464449,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06579371397564265,"score_gpt":0.3568256898022525,"score_spread":0.2910319758266098,"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."}}