>>>>> "Richard" == Richard Fateman <fateman at cs.berkeley.edu> writes:
Richard> in commercial macsyma
Richard> After setting intanalysis:false,
What happens if intanalysis has the default value of true?
Richard> and saying that k is an integer and positive,
Richard> I got these answers...
Richard> [(( - ((sqrt(3) * %i)/2) - (1/2)) * 2^((2 * %i + 4)/3) * G(((2 * %i +
Richard> 4)/3))/3),
Richard> ((2 * 2^(1/3) * (((sqrt(3) * %i)/2) - (1/2)) * G((1/3)))/9),
Richard> ((2 * %i)/3),
Assuming G here means the gamma function, then these 3 seem to be
wrong, based on the derivation in Wang's thesis, p 84-85.
Wang says integrate(x^m*exp(%i*k*x^n),x,0,inf) is
exp(signum(k)*%i*%pi*(m+1)/(2*n))*gamma(s/n/(abs(k))^s)
where s = (m+1)/n. I've gone over the derivation, and it looks
right.
I'm surprised that Mathematica says the integrals don't converge.
Richard> integrate(((x^k * log(x))/(x + 3)),x,0,inf)]
Wang says for k /= 0 and -1 < k < 1, this integral converges and can
be expressed in terms of the beta function and its derivatives. I
haven't examined that yet.
Thanks, everyone, who evaluated the integrals for me,
Ray