A new one-parameter deformation of the exponential function

G. Kaniadakis and A.M. Scarfone

Physica A: Statistical Mechanics and its Applications, 2002, vol. 305, issue 1, 69-75

Abstract: Recently, in Kaniadakis (Physica A 296 (2001) 405), a new one-parameter deformation for the exponential function exp{κ}(x)=(1+κ2x2+κx)1/κ; exp{0}(x)=exp(x), which presents a power-law asymptotic behaviour, has been proposed. The statistical distribution f=Z−1exp{κ}[−β(E−μ)], has been obtained both as stable stationary state of a proper nonlinear kinetics and as the state which maximizes a new entropic form. In the present contribution, starting from the κ-algebra and after introducing the κ-analysis, we obtain the κ-exponential exp{κ}(x) as the eigenstate of the κ-derivative and study its main mathematical properties.

Keywords: Deformed exponential function; Deformed algebra; Deformed statistical distribution (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:305:y:2002:i:1:p:69-75

DOI: 10.1016/S0378-4371(01)00642-2

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