计算级数时除以零误差

Question

我正在尝试计算一个序列，但我运行遇到了一个我不知道为什么会发生的问题。

“运行时警告：在 double_scalars”中遇到被零除的问题

我查了下代码，好像没有什么奇点，所以一头雾水。这是当前的代码（log 代表自然对数）（编辑：扩展代码如果有帮助）：

from numpy import pi, log


#Create functions to calculate the sums

def phi(z: int):
    k = 0
    phi = 0

    #Loop through 1000 times to try to approximate the series value as if it went to infinity

    while k <= 100:
        phi += ((1/(k+1)) - (1/(k+(2*z))))
        k += 1

    return phi

def psi(z: int):
    psi = 0
    k = 1

    while k <= 101:
        psi += ((log(k))/( k**(2*z)))
        k += 1
    
    return psi

def sig(z: int):
    sig = 0
    k = 1

    while k <= 101:
        sig += ((log(k))**2)/(k^(2*z))
        k += 1

    return sig

def beta(z: int):
    beta = 0
    k = 1

    while k <= 101:
        beta += (1/(((2*z)+k)^2))
        k += 1
    
    return beta


#Create the formula to approximate the value. For higher accuracy, either calculate more derivatives of Bernoulli numbers or increase the boundry of k.

def Bern(z :int):
    #Define Euler–Mascheroni constant

    c = 0.577215664901532860606512

    #Begin computations (only approximation)

    B = (pi/6) * (phi(1) - c - 2 * log(2 * pi) - 1) - z * ((pi/6) * ((phi(1)- c - (2 * log(2 * pi)) - 1) * (phi(1) - c) + beta(1) - 2 * psi(1)) - 2 * (psi(1) * (phi(1) - c) + sig(1) + 2 * psi(1) * log(2 * pi)))

    #output

    return B

A = int(input("Choose any value: "))
print("The answer is", Bern(A + 1))

如有任何帮助，我们将不胜感激。

Answer 1

您确定需要 ^ 位异或 运算符而不是 ** 吗？我已经尝试使用输入参数 z = 1 运行你的代码。在第二次迭代中，k^(2*z) 的结果等于 0，所以零除法误差来自哪里 (2^2 *1 = 0).

计算级数时除以零误差

Division by Zero error in calculating series

math

numpy

divide-by-zero