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Entropy 2013, 15(12), 5144-5153; doi:10.3390/e15125144

The κ-Generalizations of Stirling Approximation and Multinominal Coefficients

1,*  and 2
1 Department of Electrical and Electronic Engineering, Ibaraki University, 4-12-1 Nakanarusawa,Hitachi, Ibaraki 316-8511, Japan 2 Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi, Inage, Chiba, Chiba 263-8522, Japan
* Author to whom correspondence should be addressed.
Received: 20 August 2013 / Revised: 20 November 2013 / Accepted: 21 November 2013 / Published: 26 November 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
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Stirling approximation of the factorials and multinominal coefficients are generalized based on the κ-generalized functions introduced by Kaniadakis. We have related the κ-generalized multinominal coefficients to the κ-entropy by introducing a new κ-product operation, which exists only when κ ≠ 0.
Keywords: κ-entropy; κ-exponential; κ-logarithm; Stirling approximation κ-entropy; κ-exponential; κ-logarithm; Stirling approximation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Wada, T.; Suyari, H. The κ-Generalizations of Stirling Approximation and Multinominal Coefficients. Entropy 2013, 15, 5144-5153.

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