## The Expected Logarithm of a Noncentral Chi-Square Random VariableIn my Ph.D. thesis I have published a closed-form expression for the expected value of the logarithm of a noncentral chi-square random variable with even degrees of freedom. Recently I have now been able to generalize this to the expected value of the logarithm and also to negative integer moments of a noncentral chi-square random variable with arbitrary (i.e., even or odd) degrees of freedom. Moreover, I have found tight elementary upper and lower bounds to this expression. Details can be found in
## KeywordsChi-square, chi-squared, negative moments, noncentral chi-square, noncentral chi-squared, expected logarithm, Rayleigh, Rice, Ricean, Rician. ## GeneralizationsThe following lemma has been proven in (Appendix A, Lemma 3)
where is an matrix with entries
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