bacovia/t/zeta_2n.sf

#!/usr/bin/ruby

include('../lib/bacovia.sf')

const τ = (Log(-1) * -2i)

func zeta_2n(n) {
    (-1)**(n+1) * bernoulli(2*n) * τ**(2*n) / ((2*n)! * 2)
}

var output = <<'EOT'.lines
zeta(2) = ((1/24) * (-4 * log(-1)^2))
zeta(4) = ((1/1440) * (16 * log(-1)^4))
zeta(6) = ((1/60480) * (-64 * log(-1)^6))
zeta(8) = ((1/2419200) * (256 * log(-1)^8))
zeta(10) = ((1/95800320) * (-1024 * log(-1)^10))
EOT

assert_eq(gather {
    for n in (1..5) {
        var z = zeta_2n(n).simple.pretty
        say take("zeta(#{2*n}) = #{z}")
    }
}, output)