new defint.lisp bug - was: new defint.lisp and radexpand:false?

"Theorem. For any real n>0, a>=0, b>0
integrate(exp(x^n),x,a,b)=((gamma_incomplete(1/n,-a^n)-gamma_incomplete(1/n,-b^n))*%e^(-(%i*%pi)/n))/n"

I think this may be right but it is not what the new defint.lisp gives.

(%i5) kill(all);
(%o0) done
(%i1) assume(a>0,b>0,b>a,n>0);
(%o1) [a > 0,b > 0,b > a,n > 0]
(%i2) load(defint);
(%o2) "C:/Maxima-5.25.1/share/maxima/5.25.1/src/defint.lisp"
(%i3) integrate(exp(x^5),x,a,b);
(%o3) (gamma_incomplete(1/5,-b^5)-gamma_incomplete(1/5,-a^5))/5
(%i4) 
F(n,a,b):=((gamma_incomplete(1/n,-a^n)-gamma_incomplete(1/n,-b^n))*%e^(-(%i*%pi)/n))/n$
(%i5) F(5,a,b);
(%o5) 
%e^-(%i*%pi/5)*(gamma_incomplete(1/5,-a^5)-gamma_incomplete(1/5,-b^5))/5

Which is a new defint.lisp bug if your formula is right.

But the calculation is not accurate to enough precision also.

(%i8) float(rectform(float(F(5,1,2))));
(%o8) 1.0571128427649482E+12 - 9.7656250000000005E-5 * %i
(%i9) taylor(exp(x^5),x,0,1700)$
(%i10) integrate(%,x)$
(%i11) float(at(%,[x=2])-at(%,[x=1]));
($o11)   1.0132394896940182E+12
(%i12) taylor(exp(x^5),x,0,2700)$
(%i13) integrate(%,x)$
(%i14) float(at(%,[x=2])-at(%,[x=1]));
(%o14) 1.0132394896940182E+12

Maybe this is a little of both, a lack of precision and a defint.lisp error.

FWIW,

Rich


-----Original Message----- 
From: Thomas D. Dean
Sent: Wednesday, January 11, 2012 2:36 PM
To: Richard Fateman
Cc: Edwin Woollett ; Maxima - list
Subject: Re: [Maxima] new defint.lisp bug - was: new defint.lisp and 
radexpand:false?

On Wed, 2012-01-11 at 10:47 -0800, Richard Fateman wrote:
> integrate(exp(x^5),x,1,2);
Maple returns

-1/5*(-1)^(4/5)*(
    (x*(-1)^(1/5)*Pi*csc(Pi/5))/(gamma(4/5)*(-x^5)^(1/5))
  - (x*(-1)^(1/5)*gamma(1/5,-x^5))/((-x^5)^(1/5))
);

gamma(m,n) is the incomplete gamma function

Tom Dean

_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima