Riemann's Zeta Function - another approach (RPL)

[Dieter]

(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?

BTW, I am now testing a Free42 version, essentially your code but with a new approximation for 0,5...1. The only problem is x=0 as the reflection formula would cause an attempt at calculating Zeta(1). Anyway, the results look quite promising once the number of terms for x>2 is sufficiently large. With about 200/x terms (a very rough estimate) the largest error I noticed for your examples above was 2 ULP.

Dieter