Expectation values for integer powers of a Poisson-distributed random number

Julian Henn
  • Acta Crystallographica Section A Foundations of Crystallography, September 2012, International Union of Crystallography
  • DOI: 10.1107/s010876731203200x

What is it about?

It is shown that expectation values of Poisson-distributed random numbers exist not only for the well known positive integer powers but also for negative integer powers. A recursion formula for the calculation of expectation values of powers differing by one is given. This recursion formula helps to find an analytical representation for both positive and negative integer powers in terms of the hypergeometric function.

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