python - ZeroDivisionError: 0.0 to a negative or complex power -

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i wanted find integral ((sin x)^8, {x,0,2*pi}) , tried write simple program, without external modules "math", calculate taylor series , summarize interval (0,2*pi) 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 negative or complex power

suddenly occurs. , don't see divided 0 or have power of complex number, variables have real positive value. "k" value both terms of series quantity , 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         l in range(2,t+1):             res=res*l                return res  def ser(a):     sin_part=a     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   in range(0,k-1):     sum+=(ser(i*2*3.1415926/k))**8 print sum

and don't see divided 0 or have power of complex number, variables have real positive value.

not true. on first iteration of 

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

you have i=0, argument ser 0, a == 0, , have (a**(2j-1)), takes 0 complex power.

maybe meant a**(2*j-1)? python uses j unit imaginary, , 2j-1 complex number.


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