Evaluation of ζ(2) by the definition (sort of) [HP42S & HP71B]

10262021, 03:24 PM
Post: #7




RE: Evaluation of ζ(2) by the definition (sort of) [HP42S & HP71B]
(10262021 02:13 PM)Ren Wrote: What does ζ mean? (10252021 01:29 PM)Albert Chan Wrote: ζ(2) = 1.65  sum(1/(k^2*(4*k^21)), k=3..inf) Only 1 term CF correction. It does help. CAS> zeta2(n) := 1.65  sum(1/(k^2*(4*k^21)), k=3..n) CAS> corr2(n) := 1/horner([12,0,4.2,0],n+0.5) CAS> zeta2(10) → 1.6450058264 CAS> Ans+corr2(10) → 1.64493406774 CAS> pi*pi/6. → 1.64493406685 

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