ZeroDivisionError: 0.0 to a negative or complex power

Question

I wanted to find an integral ((sin x)^8, {x,0,2*Pi}) and tried to write a simple program, without any external modules as "math", which calculate Taylor series and summarize it for interval (0,2*Pi) but an errors

Traceback (most recent call last):
  File "E:\python\ShAD\sin.py", line 27, in <module>
    sum+=(ser(i*2*3.1415926/k))**8
  File "E:\python\ShAD\sin.py", line 21, in ser
    sin_part+=((-1)**(j-1))*(a**(2j-1))/(fact(2*j-1))
ZeroDivisionError: 0.0 to a negative or complex power

suddenly occurs. And I just don't see where something is divided by zero or have power of complex number, all variables have only real positive value. "k" is a value both for terms of series quantity and interval (0,2*Pi) division.

sum=0
k=20
res=0

def fact(t):
    if t==0 or t==1:
        res=1

    else:
        res=1
        for l in range(2,t+1):
            res=res*l           
    return res

def ser(a):
    sin_part=a
    for j in range(2,k):
        print fact(2*j-1)
        sin_part+=((-1)**(j-1))*(a**(2j-1))/(fact(2*j-1))
        print 'yay'
    return sin_part


for i in range(0,k-1):
    sum+=(ser(i*2*3.1415926/k))**8
print sum

Answer 1

And I just don't see where something is divided by zero or have power of complex number, all variables have only real positive value.

Not true. On the first iteration of

for i in range(0,k-1):
    sum+=(ser(i*2*3.1415926/k))**8

you have i=0, so the argument to ser is 0, so a == 0, and you have (a**(2j-1)), which takes 0 to a complex power.

Maybe you meant a**(2*j-1)? Python uses j for the unit imaginary, and so 2j-1 is a complex number.