Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
French, J.B., Kota, V.K.B.: Annu. Rev. Nucl. Part. Sci.32, 35 (1982)
French, J.B.: Nucl. Phys. A396, 87 C (1983)
Brody, T.A., Flores, J., French, J.B., Mello, P.A., Pandey, A., Wong, S.S.M.: Rev. Mod. Phys.53, 472 (1981)
Kota, V.K.B.: Z. Phys. A — Atoms and Nuclei315, 91 (1984)
Draayer, J.P., French, J.B., Potbhare, V., Wong, S.S.M.: Phys. Lett.55B, 263 (1975)
Draayer, J.P., French, J.B., Wong, S.S.M.: Ann. Phys.106, 483 (1977)
Cramer, H.: Mathematical methods in statistics. Princeton, N.J.: Princeton University Press 1946
Bateman, H.: Higher transcendental functions. Vol. II. New York: McGraw-Hill Book Company, Inc. 1953
Chang, F.S., French, J.B.: Phys. Lett.44B, 131 (1973)
Kuo, T.T.S.: Nucl. Phys. A103, 71 (1967)
French, J.B., Kota, V.K.B., Pandey, A., Tomsovic, S.: (to be published)