Unbiased Estimation in the Non-central Chi-Square Distribution

We give expansions for unbiased estimators based on the arithmetic mean of an analytic function of the non-centrality parameter of the non-central chi-square distribution. The terms of these expansions depend on the derivatives of the function to be estimated and on certain polynomials which are constructed from the generalized Laguerre polynomials. We also investigate the asymptotic properties of the proposed estimators.