{"paper":{"title":"New representations of pi and Dirac delta using the nonextensive-statistical-mechanics q-exponential function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"C. Tsallis, M. Jauregui","submitted_at":"2010-03-25T18:15:15Z","abstract_excerpt":"We present a generalization of the representation in plane waves of Dirac delta, $\\delta(x)=(1/2\\pi)\\int_{-\\infty}^\\infty e^{-ikx}\\,dk$, namely $\\delta(x)=(2-q)/(2\\pi)\\int_{-\\infty}^\\infty e_q^{-ikx}\\,dk$, using the nonextensive-statistical-mechanics $q$-exponential function, $e_q^{ix}\\equiv[1+(1-q)ix]^{1/(1-q)}$ with $e_1^{ix}\\equiv e^{ix}$, being $x$ any real number, for real values of $q$ within the interval $[1,2[$. Concomitantly with the development of these new representations of Dirac delta, we also present two new families of representations of the transcendental number $\\pi$. Incident"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4967","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}