{"id":"W2413928708","doi":"10.1017/s0025557200003582","title":"95.50 Fractional-power identities for Fibonacci and Lucas polynomials and numbers","year":2011,"lang":"en","type":"article","venue":"The Mathematical Gazette","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Royal Ottawa Mental Health Centre; Royal Military College of Canada","funders":"","keywords":"Fibonacci number; Lucas number; Fibonacci polynomials; Mathematics; Lucas sequence; Power (physics); Combinatorics; Orthogonal polynomials; Classical orthogonal polynomials; Physics","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001935038,0.0001353547,0.0002052262,0.00001218409,0.0002218506,0.00005182067,0.0001100969,0.00002802623,0.001208974],"category_scores_gemma":[0.00003827141,0.0000892145,0.000065632,0.00004079722,0.0002434351,0.0001094589,0.0000800742,0.00008688984,0.00005961591],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005119131,"about_ca_system_score_gemma":0.00000740966,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006591331,"about_ca_topic_score_gemma":2.225301e-7,"domain_scores_codex":[0.9993089,0.00001603646,0.0002269652,0.0001640083,0.00008812716,0.0001959857],"domain_scores_gemma":[0.998915,0.0006749464,0.00008148632,0.0002199865,0.00002952425,0.00007907757],"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":[0.00001227471,0.00005540022,0.00003512383,0.00003044127,0.0000420935,8.782968e-8,0.0006789759,3.736608e-7,0.0001214681,0.9969689,0.001384604,0.0006702565],"study_design_scores_gemma":[0.0001937866,0.00001989049,0.000119145,0.00002162905,0.00005102159,0.000005129033,0.0009726268,0.0001539707,0.0005134097,0.9926822,0.005146903,0.0001202872],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.127959,0.0001980511,0.7433919,0.001667617,0.0000986959,0.001166122,0.0001092676,0.00008197353,0.1253274],"genre_scores_gemma":[0.9647188,0.00001249258,0.03072268,0.0002427519,0.0001817221,0.0003557423,0.00000579092,0.00003496885,0.003725066],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8367598,"threshold_uncertainty_score":0.9997041,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02421252764736043,"score_gpt":0.2747399671771949,"score_spread":0.2505274395298345,"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."}}