{"id":"W4415214541","doi":"10.1016/j.matcom.2025.10.014","title":"Modified Levin formulation for highly oscillatory Bessel integral transforms","year":2025,"lang":"en","type":"article","venue":"Mathematics and Computers in Simulation","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"Shenzhen Science and Technology Innovation Program; National Key Research and Development Program of China; National Natural Science Foundation of China","keywords":"Bessel function; Helmholtz equation; Radial basis function; Interpolation (computer graphics); Computation; Quadrature (astronomy); Helmholtz free energy; Integral equation; Basis function","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":[0.0005481993,0.0002022414,0.0003983647,0.0002611543,0.0001124672,0.00008247554,0.0001021446,0.0001450856,0.000008754456],"category_scores_gemma":[0.0002053459,0.0001697794,0.0001060543,0.0002306183,0.00002683954,0.0001520346,0.00003422648,0.0001028327,0.000001243731],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000678517,"about_ca_system_score_gemma":0.00002907422,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005198134,"about_ca_topic_score_gemma":0.00001462266,"domain_scores_codex":[0.998705,0.00002217627,0.0006767731,0.0002338323,0.0001426073,0.0002196296],"domain_scores_gemma":[0.9977052,0.001808794,0.0001198639,0.0002379175,0.00008231963,0.00004589723],"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":[0.00006000145,0.0001988161,0.00007798689,0.00108838,0.00003459841,4.050932e-7,0.001241167,0.005907899,0.00005768957,0.9800013,0.0001475944,0.01118416],"study_design_scores_gemma":[0.0005937871,0.00003105441,0.0001212797,0.0002093949,0.0000302195,5.134457e-7,0.00007432282,0.4956377,0.00003795536,0.5028364,0.0003192817,0.000108074],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2692447,0.00004354937,0.7270312,0.0001428057,0.0002039858,0.000812125,0.000009271442,0.00006319107,0.002449179],"genre_scores_gemma":[0.8829495,0.000007018478,0.1165094,0.00007861065,0.00004259212,0.0001040962,0.00000890613,0.00001850501,0.0002813759],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6137048,"threshold_uncertainty_score":0.6923403,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04774971287898049,"score_gpt":0.3338365930760027,"score_spread":0.2860868801970222,"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."}}