[math-fun] Probability of a real polynomial's having all roots real

Let c = (c_0,...,c_(n-1)) have the standard normal distribution on R^n, i.e., the c_k are independent real random variables, each with probability density given by d(x) = (1/(sqrt(2 pi)) exp(-x^2 / 2)) QUESTION: Find the probability f(n) that the polynomial P(x) = x^n + c_(n-1) x^(n-1) + ... + c_1 x + c_0 has all its roots real ? (It's easy to find an integral expression for f(2), but not a closed form.) Better yet, find an asymptotic expression for f(n) as n -> oo . --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele