def diff(x,order=1,period=None, _cache=_cache):
    """
    Return k-th derivative (or integral) of a periodic sequence x.

    If x_j and y_j are Fourier coefficients of periodic functions x
    and y, respectively, then::

      y_j = pow(sqrt(-1)*j*2*pi/period, order) * x_j
      y_0 = 0 if order is not 0.

    Parameters
    ----------
    x : array_like
        Input array.
    order : int, optional
        The order of differentiation. Default order is 1. If order is
        negative, then integration is carried out under the assumption
        that ``x_0 == 0``.
    period : float, optional
        The assumed period of the sequence. Default is ``2*pi``.

    Notes
    -----
    If ``sum(x, axis=0) = 0`` then ``diff(diff(x, k), -k) == x`` (within
    numerical accuracy).

    For odd order and even ``len(x)``, the Nyquist mode is taken zero.

    """
    tmp = asarray(x)
    if order is 0:
        return tmp
    if iscomplexobj(tmp):
        return diff(tmp.real,order,period)+1j*diff(tmp.imag,order,period)
    if period is not None:
        c = 2*pi/period
    else:
        c = 1.0
    n = len(x)
    omega = _cache.get((n,order,c))
    if omega is None:
        if len(_cache) > 20:
            while _cache:
                _cache.popitem()

        def kernel(k,order=order,c=c):
            if k:
                return pow(c*k,order)
            return 0
        omega = convolve.init_convolution_kernel(n,kernel,d=order,
                                                 zero_nyquist=1)
        _cache[(n,order,c)] = omega
    overwrite_x = _datacopied(tmp, x)
    return convolve.convolve(tmp,omega,swap_real_imag=order % 2,
                             overwrite_x=overwrite_x)
dataset/ETHPy150Open scipy/scipy/scipy/fftpack/pseudo_diffs.py/diff/operator `==` -> `is`