New representations of π and Dirac delta using the nonextensive-statistical-mechanics q-exponential function

DOI10.1063/1.3431981zbMath1311.46039arXiv1003.4967OpenAlexW3101285080MaRDI QIDQ5251270

Max Jauregui, Constantino Tsallis

Publication date: 19 May 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4967

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (19)

Derivation of density operators for generalized entropies with quantum analysis ⋮ Extension of inverse \(q\)-Fourier transform via conformal mapping ⋮ Reflections on the \(q\)-Fourier transform and the \(q\)-Gaussian function ⋮ Derivation of the density operator with quantum analysis for the generalized Gibbs ensemble in quantum statistics ⋮ \(Q\)-Fourier transform and its inversion-problem ⋮ The nonadditive entropy \(S_q\) and its applications in physics and elsewhere: some remarks ⋮ \(q\)-generalization of the inverse Fourier transform ⋮ Statistical field theory of a nonadditive system ⋮ Note on aq-modified central limit theorem ⋮ A fractional Fokker–Planck equation for non-singular kernel operators ⋮ Phase transition for the system of finite volume in the ϕ4 theory in the Tsallis nonextensive statistics ⋮ SOME OPEN POINTS IN NONEXTENSIVE STATISTICAL MECHANICS ⋮ Nonlinear quantum equations: Classical field theory ⋮ Entropic forms and related algebras ⋮ Travelling-wave and separated variable solutions of a nonlinear Schroedinger equation ⋮ On a conjecture about Dirac’s delta representation using q-exponentials ⋮ A direct proof of Jauregui-Tsallis’ conjecture ⋮ Integral representation of Dirac distribution using the Tsallis q-exponential function ⋮ On formulas for π experimentally conjectured by Jauregui–Tsallis

Cites Work

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• Defect turbulence and generalized statistical mechanics
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• Renormalization in general gauge mediation
• On non-Gaussianity and dependence in financial time series: a nonextensive approach
• Introduction to Nonextensive Statistical Mechanics
• On aq-generalization of circular and hyperbolic functions
• Generalization of symmetric α-stable Lévy distributions for q>1
• Self-organization in dissipative optical lattices

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