Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(07-09-2017 09:59 PM)Dieter Wrote:  Update: After a quick and dirty re-evaluation of the Zeta reference, maybe you want to try this new coefficient set:

c0 =   0,577215664858
c1 =   0,07281584127
c2 = –0,004845236649
c3 = –0,000342578367
c4 =   0,000096238267
c5 = –0,000007418588
c6 = –0,000000822161

Now Zeta(0,1) should return –0,603037519853 which is only 3 ULP off.

Done:

0.0 -> -.5
0.1 -> -.60303751985(3) [6]
0.2 -> -.73392092489(8) [6]
0.3 -> -.90455925725(7) [4]
0.4 -> -1.1347977838(5) [7]
0.5 -> -1.460354508(77) [81]
0.6 -> -1.9526614482(0) [2]
0.7 -> -2.7783884455(8) [5]
0.8 -> -4.4375384159(3) [0]
0.9 -> -9.430114019(36) [40]
0.95 -> -19.4264371969
1.00 -> 9.99999999999E499
1.05 -> 20.58084430(16) [20]

I can only praise your striving for perfection!

Gerson.

Edited to fix (yet another) typo.