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- #!/usr/bin/ruby
- # Daniel "Trizen" Șuteu
- # Date: 20 May 2017
- # https://github.com/trizen
- # A very fast converging series for zeta(3).
- # The formula is:
- # zeta(3) = -8*pi^2/14 * (log(27/16) + Sum_{n>=0}(zeta(2n) - 1)/((2n + 1) * (2n + 2) * 2^(2n)))
- # The formula is based on the following two formulas:
- # -14*zeta(3) / (8*pi^2) = Sum_{n>=0} zeta(2n)/((2n + 1) * (2n + 2) * 2^(2n))
- # log(27/16) = Sum_{n>=0} 1/((2n + 1) * (2n + 2) * 2^(2n))
- var sum = log(27/16)
- for n in (0..40) {
- sum += (zeta(2*n) - 1)/((2*n + 1) * (2*n + 2) * 2**(2*n))
- }
- var f = -(8 * Num.pi**2)/14
- say sum*f #=> 1.20205690315959428539973816151144999076498629234
- say zeta(3) #=> 1.20205690315959428539973816151144999076498629234
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