test_gosper.py 文件源码

def test_gosper_sum_AeqB_part2():
    f2a = n**2*a**n
    f2b = (n - r/2)*binomial(r, n)
    f2c = factorial(n - 1)**2/(factorial(n - x)*factorial(n + x))

    g2a = -a*(a + 1)/(a - 1)**3 + a**(
        m + 1)*(a**2*m**2 - 2*a*m**2 + m**2 - 2*a*m + 2*m + a + 1)/(a - 1)**3
    g2b = (m - r)*binomial(r, m)/2
    ff = factorial(1 - x)*factorial(1 + x)
    g2c = 1/ff*(
        1 - 1/x**2) + factorial(m)**2/(x**2*factorial(m - x)*factorial(m + x))

    g = gosper_sum(f2a, (n, 0, m))
    assert g is not None and simplify(g - g2a) == 0
    g = gosper_sum(f2b, (n, 0, m))
    assert g is not None and simplify(g - g2b) == 0
    g = gosper_sum(f2c, (n, 1, m))
    assert g is not None and simplify(g - g2c) == 0