Bivariate distributions in statistical spectroscopy studies

Orthogonal polynomials in two variables, defined by a bivariate density function, are used to derive series expansions for expectation values with respect to the two variables. The convergence of the resulting polynomial expansion is due to the action of a central limit theorem. The shell model results for fixedE, J occupancies in (ds) ^m=5T=1/2 space are compared with the polynomial expansion results and the agreement is good.