where H ′ ′ ( μ μ ) is used to denote the derivative of H ( ε ε ) evaluated at ε ε = μ μ and where the O ( x n ) notation refers to limiting behavior of order x n . The expansion is only valid if H ( ε ε ) vanishes as ε ε → → − − ∞ ∞ and goes no faster than polynomially in ε ε as ε ε → → ∞ ∞ . If the integral is from zero to infinity, then the integral in the first term of the expansion is from zero to μ μ and the second term is unchanged.