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- #!/usr/bin/ruby
- #
- ## Closed-form for Zeta(2n)
- #
- # See also: https://en.wikipedia.org/wiki/Riemann_zeta_function
- func bernoulli_number(n) is cached {
- n.is_one && return 1/2
- n.is_odd && return 0
- ^n -> reduce({|a, k| a - (__FUNC__(k) * binomial(n, k) / (n - k + 1))}, 1)
- }
- func zeta_2n(Number n {.is_even}) {
- ((-1)**(n/2 + 1) * 2**(n - 1) * Num.pi**n * bernoulli_number(n)) / n!
- }
- for n in (1 .. 10) {
- say "zeta(#{2*n}) = #{zeta_2n(2*n)}"
- }
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