stack lift and change sign

[Thomas Klemm]

There was a recent thread where someone pointed to an exercise with the following recursive definition:
\[
u_1=\frac{3}{2} \\
u_{n+1}=\frac{n u_n + 1}{2(n+1)}
\]
For this sequence we can find a closed formula:
\[u_n=\frac{2^{-n}+1}{n}\]

This is the program I came up with:

ENTER
CHS
2
X<>Y
Y^X
1
+
X<>Y
/

Everything went fine with the HP-15c until I tried to calculate \(u_0\). My expectation was to get an error but alas I got different results. Thus I tried to find the reason: it appears that CHS doesn't enable the stack lift if the value in register X is 0.


All this lead me to the following test-case:

a
ENTER
CHS
b

For a and b I used different values:

a = 7, b = 2
\[\begin{matrix}
Model & X & Y & Z & T \\
35 & -2 & 7 & * & * \\
45 & 2 & 7 & * & * \\
15c & 2 & -7 & 7 & * \\
41c & 2 & -7 & 7 & * \\
\end{matrix}\]

a = 0, b = 2
\[\begin{matrix}
Model & X & Y & Z & T \\
35 & -2 & 0 & * & * \\
45 & 2 & 0 & * & * \\
15c & 2 & 0 & * & * \\
41c & 2 & 0 & 0 & * \\
\end{matrix}\]

It appears that this behavior changed over time in HP-calculators.

Cheers
Thomas