[01] Julian Henn, Bayreuth, Germany.

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.

Poisson Distribution, Negative Powers, Hypergeometric Function, Generalized Hypergeometric Function

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