# [Maxima] new defint.lisp bug - was: new defint.lispandradexpand:false?

Richard Hennessy rich.hennessy at verizon.net
Fri Jan 13 14:32:09 CST 2012

I succeeded (partially), when x is negative and n is an even integer then
this is not real valued.  I hope this clarifies everything.  I want to add
one last thing.  It was not worth the time.  As Edwin Woollett pointed out
(-1)^(4/5) is not numerically equal to 1 but Maxima evaluated it to one
anyway, which is a bug I guess and I don’t know if anyone is planning on
fixing it.  Does everyone have no problem with this?

Rich

-----Original Message-----
From: Richard Hennessy
Sent: Friday, January 13, 2012 3:10 PM
To: Rupert Swarbrick
Cc: Maxima List
Subject: Re: [Maxima] new defint.lisp bug - was: new

"Are you claiming that you have a function that is not continuous but is an
antiderivative of exp(x^7)?"

No, I am claiming that this function below is piecewise defined but
continuous anyway and is real valued and is an antiderivative of exp(x^n)
when n > 0, n is real and x is real.  When n is an odd integer > 0 then it
also is real valued antiderivative for all real x both positive and
negative.  I used Aleksas Domarkas' answer for the positive piece, I just
spliced the negative and positive answers into one function, which could
also be done with "if then else" if you like that better.  My goal was to
get one expression for the antiderivative which was true and real valued for
all x and integer n>2.  I succeeded.

integrate(exp(x^n),x);
(-gamma_incomplete(1/n,-x^n)*%e^-(%i*%pi/n)/n+gamma(1/n)*%e^-(%i*%pi/n)/n+gamma(1/n)/n)*(signum(x)+1)/2
+gamma_incomplete(1/n,-x^n)*(1-signum(x))/(2*n)

Rich

-----Original Message-----
From: Rupert Swarbrick
Sent: Thursday, January 12, 2012 7:45 PM
To: maxima at math.utexas.edu
Subject: Re: [Maxima] new defint.lisp bug - was: new