{"id":"W2029727657","doi":"10.1063/1.1866222","title":"Partial fractions expansions and identities for products of Bessel functions","year":2005,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Bessel function; Bessel polynomials; Struve function; Mathematics; Bessel process; Cylindrical harmonics; Taylor series; Series (stratigraphy); Algebraic number; Series expansion; Mathematical analysis; Order (exchange); Bessel's inequality; Hankel transform; Pure mathematics; Orthogonal polynomials; Gegenbauer polynomials; Classical orthogonal polynomials","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":[0.0006276251,0.0001578499,0.0005737178,0.00008442452,0.0001444246,0.00003875103,0.0001216985,0.00007605298,0.0001281324],"category_scores_gemma":[0.001962436,0.0001190738,0.0002289419,0.0001565843,0.0001382011,0.0003608515,0.00003822245,0.0001912844,0.00001344299],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002618656,"about_ca_system_score_gemma":0.00008474584,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.727742e-7,"about_ca_topic_score_gemma":6.88933e-7,"domain_scores_codex":[0.9983417,0.00004427476,0.0009862962,0.0001178149,0.0003171142,0.000192844],"domain_scores_gemma":[0.9966325,0.001904025,0.000586907,0.0002542072,0.0005003362,0.0001220064],"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":[0.00007839633,0.001944234,0.00001452921,0.001365556,0.0002759118,0.000001060369,0.001244082,0.00006353462,0.006111088,0.9416875,0.04394393,0.003270126],"study_design_scores_gemma":[0.0006994609,0.0002632904,0.00001357435,0.0002512295,0.0005255215,0.00009454343,0.0006401684,0.001277363,0.01132758,0.9788681,0.005874651,0.0001645447],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2578064,0.000175863,0.7356635,0.002279117,0.000400559,0.0006111551,0.00006485346,0.00003752255,0.00296111],"genre_scores_gemma":[0.7440385,0.00005687021,0.2500217,0.00007582861,0.002282935,0.00005309664,0.000003008264,0.00006073654,0.003407322],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4862321,"threshold_uncertainty_score":0.485569,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0691443857402608,"score_gpt":0.3352390692696268,"score_spread":0.2660946835293659,"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."}}