<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def mean_second_derivative_central(x):
 """ Returns the mean value of a central approximation of the second derivative .. math:: \\frac{1}{n} \\sum_{i=1,\ldots, n-1} \\frac{1}{2} (x_{i+2} - 2 \\cdot x_{i+1} + x_i) :param x: the time series to calculate the feature of :type x: numpy.ndarray :return: the value of this feature :return type: float """


    diff = (_roll(x, 1) - 2 * np.array(x) + _roll(x, -1)) / 2.0
    return np.mean(diff[1:-1])