Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(06-30-2017 12:08 PM)Paul Dale Wrote:  How does this compare to Jean-Marc Baillard's implementation of Borwein's second algorithm?

Quoting from your first link:

Quote:      3 XEQ "ZETA"   >>>>     Zeta(3)     = 1.202056903                   ---Execution time = 21s--- 
  -7.49 XEQ "ZETA"   >>>>     Zeta(-7.49) = 0.003312040169                ---Execution time = 24s--- 
    1.1 XEQ "ZETA"   >>>>     Zeta(1.1)   = 10.58444847                   ---Execution time = 21s---

   3  XEQ "ZETA" ->  1.202056903    (15 s) [HP-41CV]
-7.49 GSB    B   ->  0.003312040168 (26 s) [HP-15C] (probably 11 seconds on the HP-41CV)
 1.1  XEQ "ZETA" -> 10.58444846     (34 s) [HP-41CV]


This relies on an empirical correction expression I've found, though:

1/(2*((n + 1/2 + (s + 1)/(8*n) - (2*s + 1)/(24(?)*n^2) + ... )^x))

But I am still not sure wheter the last term is correct or if this is correct at all...

Gerson.

PS: Perhaps Borwein's algorithm is overkill for the HP-41. If more digits are to be calculated, as on the wp34s, then is should be faster, even if more terms of the correction expression were available.