Abstract
In this paper the deformed boson algebra giving the Gentile distribution function is constructed by using the model of ideal gas of deformed bosons and some properties of a root of unity. As an example we discuss the quantum optical problem related to the Gentile (or f-deformed) boson algebra with large but finite M. For this algebra we construct the Gentile (or f-deformed) coherent state and discuss its nonclassical properties such as sub-Poissonian statistics and anti-bunching effect.
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