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 ...
