Okay, maybe you can't use my function for non real limits of integration and
say integrate(exp(-x^4),x,a,b) = F(b)-F(a) when b and a are not real. In
the case that they are real you can use it.
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