Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral χ2-distributed random variable are presented in the cases of both even and odd degrees of freedom. Moreover, some basic properties of these expectations are derived and tight upper and lower bounds on them are proposed.
Keywords: central χ2 distribution; chi-square distribution; expected logarithm; exponential distribution; negative integer moments; noncentral χ2 distribution; squared Rayleigh distribution; squared Rice distribution.