Laguerre series forms of non-central X2 and F distributions

Abstract

Fisher (1928) expressed the distribution function of the non-central %2 in terms of Bessel functions with imaginary argument. Wishart (1932) and Tang (1938) evaluated the probability integrals of the non-central %2 and F distributions; they involve a heavy amount of labour. In this paper Laguerre series expansions of these distributions are derived. In ? 2 series expansions of the distributionp (X) of X = ,y'2 (denoting a non-central chi-squared by x'2) is developed in terms of Laguerre polynomials, namely