def forward_difference(y):

    n = len(y)

    delta = np.zeros((n, n))

    delta[:, 0] = y

    for i in range(1, n):

        for j in range(n - i):

            delta[j, i] = delta[j + 1, i - 1] + delta[j, i - 1]

    return delta

def forward_difference(y):

    n = len(y)

    delta = np.zeros((n, n))

    delta[:, 0] = y

    for i in range(1, n):

        for j in range(n - i):

            delta[j, i] = delta[j, i - 1] - delta[j + 1, i - 1]

    return delta

def forward_difference(y):

    n = len(y)

    delta = np.zeros((n, n))

    delta[:, 0] = y

    for i in range(1, n):

        for j in range(n - i):

            delta[j, i] = delta[j + 1, i] - delta[j, i]

    return delta

def forward_difference(y):

    n = len(y)

    delta = np.zeros((n, n))

    delta[:, 0] = y

    for i in range(1, n):

        for j in range(n - i):

            delta[j, i] = delta[j - 1, i - 1] - delta[j, i - 1]

    return delta

def forward_difference(y):

    n = len(y)

    delta = np.zeros((n, n))

    delta[:, 0] = y

    for i in range(1, n):

        for j in range(n - i):

            delta[j, i] = delta[j + 1, i - 1] - delta[j, i - 1]

    return delta

n+1

n-1

n

2n

2n-1

The code does not include necessary import statements.

The method is not applicable for non-polynomial functions.