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Recently, in Kaniadakis (Physica A 296 (2001) 405), a new one-parameter deformation for the exponential function exp _{κ}(x)=( 1+κ ²x ²+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.