Considering my last question ('Problem with hypergeometric') I tried to replace my Ansatz with a different formula. Here what happened:
F = lambda z: (2/pi)*integral((4*cos(x)^2-1)^z*sin(x)^2,x,0,pi)
print F(1/2)
RuntimeError: ECL says: Error executing code in Maxima:
With Maple:
F := z -> (2/Pi)*int((4*cos(x)^2-1)^z*sin(x)^2,x=0..Pi);
evalf(F(1/2)); .3697166864+.4838437554*I
Oh mei oh mei ...
This is definitely an issue. Looks like you can do it by integrating the real and imaginary parts separately:
a=numerical_integral(real(2/pi*(4*cos(x)^2-1)^(.5)*sin(x)^2),0,pi)
b=numerical_integral(imag(2/pi*(4*cos(x)^2-1)^(.5)*sin(x)^2),0,pi)
a[0]+b[0]*i
Asked: 2015-06-29 14:59:58 +0100
Seen: 218 times
Last updated: Jun 29 '15
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Well, SymPy and Fricas can't solve it either.