HP49/50 summation weirdness

[J-F Garnier]

I was comparing some results of the recent Valentin's SRC #016, and found a problem with Gerson's results I can't explain.
It's about the summation function ∑ of the HP49/50, as I'm not an expert of these machines, I would like to ask for confirmation.

I narrowed the problem to this:
compute sum(n=1,100,lnp1(-1/(100*n²)))

Doing:
'∑(N=1.,100.,LNP1(-(1./(100.*SQ(n)))))' EVAL
I get: -1.64042967882E-2

But doing:
« 0. 1. 100. FOR N
N SQ 100. * INV NEG LNP1 +
NEXT »
I get: -1.64042967918E-2

This last value is the correct one, as checked on the 71B:
>S=0 @ FOR N=1 TO 100 @ S=S+LOGP1(-1/N/N/100) @ NEXT N @ DISP S
-1.64042967918E-2
and on Free42:
-1.64042967918(5157)e-2

Is there a known problem with the 49G/50G summation function?

I used a HP49G+ rev. 2.01-2. (I don't have more recent RPL models).
Can it be reproduced on other machines?

Edit: I just checked that a 48G+ (ROM rev.R) gives the correct result for
'∑(N=1,100,LNP1(-1/(100*SQ(n))))' EVAL
-1.64042967918E-2

J-F

[rawi]

Your results are confirmed with HP50g.
It seems as if in summation lnp1(x) is transformed to ln(1+x), but not in programs.

If I do '∑(N=1.,100.,LN(1.-(1./(100.*SQ(n)))))' EVAL I get -1.64042967882E-2,
so there is no change compared to using lnp1(x)

If I do
« 0. 1. 100. FOR N
N SQ 100. * INV NEG 1 + LN +
NEXT »
I get -1.64042967882E-2.

[DavidM]

(03-18-2024 09:56 AM)J-F Garnier Wrote:  Is there a known problem with the 49G/50G summation function?

The issue you're seeing stems from the internal implementation of the Σ command, and was discussed once here in a different context.

Σ is hard-wired to pass its expression to the 50g's CAS for simplification, which in this case appears to rewrite LNP1 as LN(<expression>+1). While understandable from a symbolic viewpoint, this particular approach obviously loses the additional precision that LNP1 provides.

Sigh. This is a great example of how that forced simplification can be problematic.

[John Keith]

Also another reason that I prefer straight RPL code to algebraic expressions, the main reason being speed.