Possible bug - wrong integral for exp(-k*t)/sqrt(k*t)
Subject: Possible bug - wrong integral for exp(-k*t)/sqrt(k*t)
From: Kevin Ellwood
Date: Tue, 09 Mar 2004 17:37:43 -0500
Hi All
I am not to sure if this is a know issue (or if I did something wrong)
but I think I found a small bug. I was doing some work with maxima
(5.9) in which I was checking my own calculations and I discovered that
it got the wrong answer for:
(C1) integrate(exp(-k*t)/sqrt(k*t),t);
(D1) SQRT(%PI) k ERF(SQRT(k t))
The correct answer is:
SQRT(%PI) ERF(SQRT(k t)) /k
As is shown here:
(C3) derivative(sqrt(%PI)/k*erf(sqrt(k*t)),t);
- k t
%E
(D3) ---------
SQRT(k t)
Maxima got the hard part correct but failed to carry "k" through the
integration correctly. I found a few other integrals involving erf()
that had similar error in carrying constants through.
Good luck,
Kevin
--
.*.
Kevin R.J. Ellwood /V\
+-+-+-+-+-+-+ +-+-+-+-+-+ (/ \)
|g|e|n|t|o|o| |l|i|n|u|x| ( )
+-+-+-+-+-+-+ +-+-+-+-+-+ ^^_^^