{"id":"W2017582762","doi":"10.1016/j.jmaa.2004.09.051","title":"The study of dual integral equations with generalized Legendre functions","year":2005,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Legendre polynomials; Dual (grammatical number); Legendre function; Legendre transformation; Legendre's equation; Integral equation; Associated Legendre polynomials; Applied mathematics; Mathematical analysis; Orthogonal 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002966421,0.001687404,0.002109988,0.003514732,0.002117538,0.004435039,0.002295033,0.003146447,0.004508543],"category_scores_gemma":[0.008835922,0.001013835,0.001856357,0.001849973,0.005303839,0.008000114,0.00409795,0.004826821,0.0004543856],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001928956,"about_ca_system_score_gemma":0.001566084,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001685257,"about_ca_topic_score_gemma":0.00126376,"domain_scores_codex":[0.9989927,0.0004735269,0.0000482955,0.00008432103,0.0002500715,0.0001509224],"domain_scores_gemma":[0.9976001,0.0009760858,0.0003459267,0.0001995532,0.0004652654,0.0004130436],"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":[0.00001377738,0.00001920601,0.00008543763,0.00002255663,0.00000791004,0.0000803349,0.00008344256,0.001749141,0.0003138458,0.9964603,0.0003255619,0.0008385667],"study_design_scores_gemma":[0.00002937402,0.00001436536,0.0001114139,0.0000239717,0.00001011252,0.0002062449,0.000105733,0.0465868,0.0001784998,0.9514073,0.001305784,0.0000204984],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4440928,0.01010329,0.395793,0.01068387,0.002360359,0.0001095782,0.0001585443,0.0001958482,0.1365027],"genre_scores_gemma":[0.88052,0.003588372,0.0553971,0.0009700707,0.002290502,0.0001040667,0.0001702768,0.0002214868,0.05673819],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004508543,"threshold_uncertainty_score":0.01568812,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03738772386344857,"score_gpt":0.3151887989230241,"score_spread":0.2778010750595755,"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."}}