Expansions of $t$ Densities and Related Complete Integrals
Expansions of $t$ Densities and Related Complete Integrals
A class of alternatives is here presented to Fisher's (1925) expansion of Student's $t$ density function. These expansions involve Appell's polynomials; and hence, recurrence schemes are available for the coefficients. Complete integrals of products of $t$ densities are of interest as Behrens-Fisher densities (viewed as Bayesian posterior distributions: Jeffreys, 1940; …