Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(06-30-2017 06:42 AM)Dieter Wrote:  

(06-30-2017 02:20 AM)Gerson W. Barbosa Wrote:  Both your method and mine causes the series to be calculated to more terms than are really needed. For instance, Zeta(2) requires only 22 terms, but we evaluate 28 and 30 terms, respectively. A closer fit would require a longer formula, so yours presents a good compromise between size and exactness.

Yes, especially between 1 and 2,5 the calculated number of terms is higher than required. BTW, how did you determine the exact numbers here?

I tested one by one with ever higher n until I got all 10 significant digits right. I did this on the 15C LE which is 150x faster than the original one. I could have used the HP-15C iOS app as it is even faster:

0.0001 GSB A -> -0.5000919(117) (8 s, 95272 terms)

Do you intend to write a full range HP-41 version? I'll be traveling the next few days and I won't take any 41 along.

Thanks again for your great contributions, especially for your striving to always get as many significant digits as possible.

Gerson.