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

TL;DR

This paper extends Stirling's approximation and multinomial coefficients using Kaniadakis' $$-deformed functions, establishing a link with $$-entropy through a novel $$-product operation.

Contribution

It introduces a $$-generalized framework for factorials and multinomial coefficients, connecting them with $$-entropy and defining a new $$-product operation.

Findings

Derived the $$-generalized Stirling approximation.

Established the relation between $$-multinomial coefficients and $$-entropy.

Introduced a new $$-product operation for these functions.

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.