Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(08-01-2017 11:46 AM)Dieter Wrote:  

(07-31-2017 06:31 PM)Gerson W. Barbosa Wrote:  I wonder what might have caused these differences. The coefficients were copied from your HP-41C listing:

...
 60 0.007215664988       35 7.215664988 E-3
...
140 0.007215664464      119 7.215664464 E-3

I just found that this might be the reason why your result for x=0 is not exactly –0,5 and others may be slightly off as well: for instance Zeta(0,5) and Zeta(2) should return the exact 12-digit values -1.46035450881 and 1,64493406685, actually Free42 returns even 13 correct digits here.

On Free42 (and I suppose on a real hardware 42s) you cannot enter line 60 resp. 140 as the numbers are too long and the last digit is omitted. Could you check this please and try 7.215664988 E-3 resp. 7.215664464 E-3 here?

Bingo! Now I get -0.5 exactly. Actually, Free 42 accepts numbers with more than 30 digits.

Have to leave now. Will comment later.

Gerson.

PS: Here is the table after the suggested modifications:

 2     R/S    -->   1.64493406685      
 1.5   R/S    -->   2.61237534868      (9) 
 0.5   R/S    -->  -1.46035450879     (81)
 0     R/S    -->  -0.500000000000
-0.5   R/S    -->  -0.207886224978     (7) 
-1     R/S    -->  -0.0833333333334    (3)

  60  7.215664988E-3 
 123 -8.47149E-7
 131  3.42683395E-4
 140  7.215664464E-3

That was difficult to detect because Emu48 shows the lines


 60 0.007215664988
140 0.007215664464

Yet they could not have been entered on the real 42S.
The .RAW file I used was exported by Free42.

From now on I'll take care when exporting Free42 .RAW files to Emu42.

Code:


00 { 45-Byte Prgm }
01▸LBL "T"
02 0.333333333333333333333333333333333
03 1/X
04 3
05 -
06 END

XEQ "T" --> 3.E-33