A new one parameter deformation of the exponential function

Abstract

Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter deformation for the exponential function ${\exp }_{{}_{\{\kappa \}}}(x)=(\sqrt{1+{\kappa }^2{x}^2}+\kappa x{)}^{1/\kappa };{\exp }_{{}_{\{0\}}}(x)=\exp (x)$, which presents a power law asymptotic behaviour, has been proposed. The statistical distribution $f=Z^{-1}{\exp }_{{}_{\{\kappa \}}}[-\beta (E-\mu )]$, has been obtained both as stable stationary state of a proper non linear kinetics and as the state which maximizes a new entropic form. In the present contribution, starting from the $\kappa$-algebra and after introducing the $\kappa$-analysis, we obtain the $\kappa$-exponential ${\exp }_{{}_{\{\kappa \}}}(x)$ as the eigenstate of the $\kappa$-derivative and study its main mathematical properties.

5 pages including 2 figures. Paper presented in NEXT2001 Meeting

References in corpus (4)

• Non Linear Kinetics underlying Generalized Statistics
• H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics
• Tails of probability density for sums of random independent variables
• Power-Law Scaling for Communication Networks with Transmission Errors

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