As V gets large the t-distribution converges to the standard normal distribution. The square of a variable with a t-distribution with v degrees of freedom has an F-distribution with (1, v) degrees of freedom. Cauchy distribution is a particular case of t-distribution with v = 1. The moment generating function for t-distribution is undefined, as there is no interval around t = 0 where it is finite.
Reference: Oxford Press Dictonary of Economics, 5th edt.