Am Dienstag, den 09.12.2008, 19:57 +0100 schrieb Dieter Kaiser:
OK I think I have got it.
Here are the results for the examples which Edwin Wollett has given:
(%i9) fresnel(x):=expand(float(integrate(sin(t^2),t,0,x)))$
(%i10) map(fresnel,[1,2,3,4,5,6,7]);
(%o10) [0.310268301723381,
0.804776489343756,
.7735625268937689,
.7471338446481144,
.5279172811653222,
.6384591893150098,
.6058869316278271]
We have to do the continued fraction expansion for a greater region of
values. On the complete negative real axis the series expansion has to
be used. But in the complex plane it is necessary to use the continued
fraction expansion when the absolute value of the argument exceeds some
threshold. I tested it for more values as we have in the test file and
had no further problems.
It is really a mess that I have not seen the range of values which
causes the wrong results and have not done the necessary tests.
Today it is to late to finish the work. Furthermore I would like to look
a second time and more carefully at the results. I have also to correct
the bigfloat routine.
Furthermore I expect we have the same problem with the exponential
integral.
Dieter Kaiser