Riemann's Zeta Function - another approach (RPL)
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07-25-2017, 04:29 PM
(This post was last modified: 07-25-2017 04:45 PM by Dieter.)
Post: #61
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RE: Riemann's Zeta Function - another approach (RPL)
(07-25-2017 04:00 PM)Gerson W. Barbosa Wrote: If it is just a copy & paste matter, would you please provide a listing? Thanks! I am currently experimenting with some adjustments to squeeze out the best possible accuracy. Here is the latest version. It includes several measures to keep intermediate results with more digits than required by the final result. That's why the constant c0 in line 35 and 119 has been decreased by 0,57 (which is added back later) so that in effect this crucial value can be given to 12 decimals. Here is the listing: Code: 01 LBL "ZETA" The program uses a polynomial approximation for 0≤x<1, another one for 1<x≤2 and your original method for x>2. Line 03 and 07 generate an error if x<0 or x=1. The steps between LBL 98 and 99 add 1/(x–1) + 0,57 while trying to preseve as much accuracy as possible. This way e.g. Zeta(1,5) carries 12 digits (...7534869) before the last addition delivers the final result 2,612375349. Dieter |
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