Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(06-19-2017 09:17 PM)Dieter Wrote:  

(06-17-2017 06:07 PM)Gerson W. Barbosa Wrote:  Here is a Q&D stack-only implementation:

I assume you calculate the value for n with a, say, heuristic method (this –1,3 and 178 thing at the beginnig). Results with errors only in the last place are as good as it gets if you cannot use any additional guard digits. For s very close to 1, maybe you can switch to a simple implemenation, just with 1/s and the Euler-Masceroni constant.

Dieter, thank you for your comment and suggestion!

Yes, I prepared a table with twelve arguments ranging from 1.5 to 25 and the respective number of terms required for the maximum possible accuracy then I simply did a curve fitting of the data on the HP-42S. My goal is something that can work on slow calculators like the HP-11C and HP-15C. Complex arguments on the latter might be a bonus, albeit limited to a narrow strip. Zeta(2) requires the evaluation of only 66 terms of the alternating series (please take a look at the updated formula and program in my previous post) and even less on 10-digit calculators, also on these the last two correction terms, of which I am not sure about, might not be necessary. I think the equivalent program for classic scientific Voyagers would run in acceptable time for all arguments.

Gerson.