International Journal of Materials Chemistry and Physics
Articles Information
International Journal of Materials Chemistry and Physics, Vol.2, No.2, Apr. 2016, Pub. Date: Jan. 18, 2016
An Application of Negative Powers of Poisson Numbers in Crystallography
Pages: 50-53 Views: 2261 Downloads: 1090
Authors
[01] Julian Henn, Bayreuth, Germany.
Abstract
The formerly introduced negative integer powers [Henn (2012). ActaCryst. A 68, 703--704] are applied to a crystallographic problem. The formal notation is slightly changed in order to simplify and unify the formal appearance. The purpose of this publication is to generalize the formalism from negative integer powers to negative real-valued powers with the help of a generalized hypergeometric function. The application demonstrates that the formalism works successfully. For all powers, the expectation values approach zero for small values of the Poisson parameter , whereas the solutions known from the literature, that all use a truncated and renormalized probability density function, approach one in this case. The truncation of the probability density function from the literature leads to a wrong result in the application.
Keywords
Poisson Distribution, Negative Powers, Hypergeometric Function, Generalized Hypergeometric Function
References
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