Improper Integrals with the HP-15C LE & CE

[J-F Garnier]

(11-18-2023 02:16 AM)DavidM Wrote:  Other results on a 50g:

\begin{array}{clrr}
\hline
{\textbf{FIX}} & {\textbf{Rounded Result}} & {\textbf{Actual Result}} & {\textbf{IERR}} \\
\hline
0 & 2. & 1.86741548121 & 1.80693901574 \\
1 & 1.9 & 1.86741548121 & .180693901574 \\
2 & 1.98 & 1.98343207731 & 1.97334339834E-2 \\
3 & 1.999 & 1.99894753972 & 1.99831015657E-3 \\
4 & 1.9999 & 1.99987053054 & 1.99978859323E-4 \\
5 & 1.99998 & 1.99998381632 & 1.9999735715E-5 \\
6 & 1.999984 & 1.99998390078 & -1.9999735715E-6 \\
7 & 1.9999839 & 1.99998390078 & -1.9999735715E-7 \\
8 & 1.99998390 & 1.99998390078 & -1.9999735715E-8 \\
9 & 1.999983901 & 1.99998390078 & -1.9999735715E-9 \\
10 & 1.9999839008 & 1.99998390078 & -1.9999735715E-10 \\
11 & 1.99998390078 & 1.99998390078 & -1.9999735715E-11 \\
\end{array}

So whichever method is used in the 50g, it doesn't appear that there's much value trying to go above FIX 6 for the display mode. At least for this example. I'll leave it to those much more knowledgeable than me for what this actually means in practice.

The negative IERR value indicates that the Romberg algorithm didn't reach the target accuracy within the sample limit (32768, or maybe 65536 - not sure).
The same cause affects Free42.
On the contrary, the 15c has (apparently) no limit for the number of samples, and keeps trying forever...

J-F