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Problem with integral

asked 2015-06-29 07:59:58 -0500

Peter Luschny gravatar image

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 ...

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Well, SymPy and Fricas can't solve it either.

rws gravatar imagerws ( 2015-06-29 08:07:47 -0500 )edit

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answered 2015-06-29 13:47:46 -0500

calc314 gravatar image

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
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rws gravatar imagerws ( 2015-06-30 01:27:01 -0500 )edit

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Asked: 2015-06-29 07:59:58 -0500

Seen: 63 times

Last updated: Jun 29 '15