digamma_function.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 14 December 2016
# https://github.com/trizen

# Simple implementation of the digamma(n) function.

# See also:
#   https://en.wikipedia.org/wiki/Digamma_function

define γ = Num.EulerGamma

func digamma(n) {
    -γ - ::sum(1 ..^ n, { |k|
        ((-1)**k / k) * binomial(n-1, k)
    })
}

func digamma_from_harmonic(n) {
    -γ + ::sum(1 ..^ n, { |k|
        1/k
    })
}

say digamma(100)                  #=> 4.60016185273808740019860558557585072686681279076853
say digamma_from_harmonic(100)    #=> 4.60016185273808740019860558557585072686681279076853