{"id":"W4382139015","doi":"10.18540/jcecvl9iss9pp16052-01e","title":"An Alternative Method for the Gamma Function derived from Natural Logarithm and Pi Function","year":2023,"lang":"en","type":"article","venue":"The Journal of Engineering and Exact Sciences","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Factorial; Gamma function; Logarithm; Function (biology); Factorial experiment; Mathematics; Euler's formula; Natural logarithm; Pi; Applied mathematics; Pure mathematics; Statistics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00221318,0.0009055402,0.0007330851,0.00440163,0.001083148,0.002209496,0.001597499,0.001278005,0.007115986],"category_scores_gemma":[0.00940802,0.0002872906,0.001457509,0.00233742,0.002029567,0.004620279,0.001902221,0.002833585,0.00325174],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001324229,"about_ca_system_score_gemma":0.00145553,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001240029,"about_ca_topic_score_gemma":0.001123095,"domain_scores_codex":[0.9986773,0.0004232744,0.000092362,0.0002732053,0.000432815,0.0001009846],"domain_scores_gemma":[0.9979661,0.000863964,0.0001279328,0.000309359,0.0006477648,0.00008504446],"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":[0.00002634861,0.00001589309,0.0003903428,0.00009437616,0.00001510593,0.0001836158,0.0002044477,0.002815379,0.002375263,0.9434919,0.003334609,0.04705272],"study_design_scores_gemma":[0.00002488948,0.00005663963,0.0004989367,0.0000877297,0.00002659347,0.001214865,0.0001033569,0.0517091,0.00420332,0.8790668,0.06294501,0.00006291447],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.003539077,0.0007432662,0.9826393,0.0004541537,0.0005621259,0.00003370678,0.00007675196,0.0002831352,0.01166853],"genre_scores_gemma":[0.1709636,0.002476563,0.7951978,0.001365646,0.001671832,0.0002710092,0.00028477,0.001024847,0.02674401],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.007115986,"threshold_uncertainty_score":0.02380538,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06397529471413936,"score_gpt":0.3602995500871709,"score_spread":0.2963242553730315,"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."}}