ON THE CHARACTERISTIC FUNCTIONS OF THE F AND t DISTRIBUTIONS
Adnan F. Ifram · 2016
SUMMARY. The characteristic function mf ? exhibits recurrence properties which enable us to obtain it in series form by making use of contour integration. For odd m and even n the series is infinite; otherwise, they are finite. The characteristic function of the tn distribution is ob tained analogously. 1. Recurrence relations If X possesses the J^m> n distribution (m, n are positive integers) (Fraser, 1958, pp. 202 203), then the characteristic function fm, n(?) of F = ? X is (/?(Jm, fw))1 0(m9 n; t)9 where n