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Bezier approximation & the points of the actual function

An approximation of the curve described on a question and its answer on Math.StackExchange

Code representation of actual function

Here's the code that produces the red dots: 
f(x, m, n) = k(m, e ** -(f_1(x, m, n) ** 2))

f_1(x, m, n) = ((x - n)/(((1 - (2 * n)) * x) + n))

k(m, x) = ((1 - e) * m * x) / (((1 - (e * m)) * x) + (m - 1))