An upper bound for the expected number of real zeros of a random polynomial

Suppose that the n + 1 coefficients of a polynomial of degree n are independent normally distributed random variables with mean 0 and variance 1. We prove that the expected number of real zeros of this polynomial is less than $\text{(}\text{2}\text{π}\text{)}\text{log}\text{n + 1.116}$, and that the constant may be reduced to 1.113 if n is even.