def _romberg_diff(b, c, k):
    """Compute the differences for the Romberg quadrature corrections.
    See Forman Acton's "Real Computing Made Real," p 143.

    :param b: R(n-1, m-1) of Rombergs method.
    :param c: R(n, m-1) of Rombergs method.
    :param k: The parameter m of Rombergs method.

    :type b: float or array[float]
    :type c: float or array[float]
    :type k: int

    :returns: R(n, m) of Rombergs method.
    :rtype: float or array[float]
    """

    tmp = 4.0**k
    diff = (tmp * c - b) / (tmp - 1.0)

    return diff