$\kappa$-generalization of Stirling approximation and multinominal coefficients

Abstract

Stirling approximation of the factorials and multinominal coefficients are generalized based on the one-parameter ($\kappa$) deformed functions introduced by Kaniadakis [Phys. Rev. E \textbf{66} (2002) 056125]. We have obtained the relation between the $\kappa$-generalized multinominal coefficients and the $\kappa$-entropy by introducing a new $\kappa$-product operation.

9 pages, no figure, RevTeX and amsmath, contribution to the 3rd NEXT-Sigma-Phi Conference, Crete, Aug. 2005