>>>>> "Raymond" == Raymond Toy <raymond.toy at ericsson.com> writes:
>>>>> "Richard" == Richard Fateman <fateman at cs.berkeley.edu> writes:
Richard> in commercial macsyma
Richard> After setting intanalysis:false,
Raymond> 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),
Raymond> Assuming G here means the gamma function, then these 3 seem to be
Raymond> wrong, based on the derivation in Wang's thesis, p 84-85.
Raymond> Wang says integrate(x^m*exp(%i*k*x^n),x,0,inf) is
Raymond> exp(signum(k)*%i*%pi*(m+1)/(2*n))*gamma(s/n/(abs(k))^s)
Raymond> where s = (m+1)/n. I've gone over the derivation, and it looks
Raymond> right.
I'm mistaken. The text in Wang's thesis is wrong. He writes the
above formula for
J = exp(-%pi*%i*(m+1)/(2*n))*integrate(R^m*exp(k*R^n),R,0,inf)
but the last integral is a gamma function and its value is
gamma((m+1)/n)/(-k)^((m+1)/n)/n. (Because k < 0 in this formula.)
With this corrected formula, maxima and Macsyma return the expected
values.
Ray