Kernel busy after integrate command
I created the following code, but when I run it it tells me "Kernel is busy (interrupt)" and it does not give me the value of x nor the value of the integral.
If I do not add the line integrate((x+1)**(n-k)*(x-1)**k, Mb, 0, 2*pi),
the code works.
var('wb w ec eb M Mb')
E = M-ec*sin(M-ec*sin(M-ec*sin(M-ec*sin(M-ec*sin(M-ec*sin(M))))))
Eb = Mb-eb*sin(Mb-eb*sin(Mb-eb*sin(Mb-eb*sin(Mb-eb*sin(Mb-eb*sin(Mb))))))
f = 2*arctan(sqrt((1+ec)/(1-ec))*tan(E/2))
fb = 2*arctan(sqrt((1+eb)/(1-eb))*tan(Eb/2))
x = -cos(wb+fb-w-f)
var('k n')
# Legendrenx(M, Mb) = (1/2**n)*sum((factorial(n)/(factorial(k)*factorial(n-k)))**2*(x+1)**(n-k)*(x-1)**k , k, 0 , n)
integrate ((x+1)**(n-k)*(x-1)**k, Mb, 0, 2*pi)
print(x)
That means that the integration never terminates, at least for the integrand given in this form. This is also true when trying integration via Maxima (default ?), Giac, Fricas and Mathematica (Wolfram engine, in the latter case).
You are running this in a notebook, right ?