Bug in limit or integrate



"you are out of luck".  Yes, if you choose not to consider this a bug then 
you are choosing to make up new math laws with no basis for it and I am out 
of luck.  Anyway, I suppose I don?t care that much if pwint gets this one 
wrong.  The help for pw just needs to be modified to say that pwint() works 
by taking the antidiff() of the integrand and evaluating it at the limits of 
integration, (or computing the limit in the case of minf, inf.)  I cannot 
try to anticipate random mathematical decisions.

Rich


-----Original Message----- 
From: Barton Willis
Sent: Sunday, January 01, 2012 9:11 AM
To: rich.hennessy at verizon.net
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Bug in limit or integrate

----"Richard Hennessy" <rich.hennessy at verizon.net> wrote: -----

>I should not have used the abs() function. This is a simpler answer and it
>does not blow up at zero.

>(gamma(1/4)/4-gamma_incomplete(1/4,x^4)/4)*signum(x);

OK, this antiderivative is valid on the reals. An antiderivative that is 
valid on the entire complex plane
is x |-> x*hypergeometric([1/4],[5/4],-x^4). But Maxima is unable to compute 
limits of hypergeometric
functions, you are out of luck if you used this antiderivative to try to 
compute integrate(exp(-x^4),x,minf,inf).

Some definite integrals of exp(-x^4) are broken:

(%i6) integrate(exp(-t^4),t,0,1);
(%o6) (%i*(gamma(1/4)-gamma_incomplete(1/4,1)))/4

--bw