local SIGMA_LIMIT = 16

function sigma(flags, callback, x)
    local sum = 0
    for n = flags.start, SIGMA_LIMIT do
        sum = sum + callback(n, x)
    end
    return sum
end

function newSigmaFunction(flags, callback)
    return setmetatable({flags = flags, callback = callback}, {
        __call = function(this, x)
            return sigma(this.flags, this.callback, x)
        end
    })
end

local MATH = {}

MATH.factorial = function(number)
    local product = 1
    for i = 1, number do
        product = product * i
    end
    return product
end

MATH.power = function(x, p)
    return x ^ p
end

MATH.cosine = newSigmaFunction({start = 0}, function(n, x)
    return (MATH.power(-1, n) * MATH.power(x, 2 * n)) / MATH.factorial(2 * n)
end)

MATH.sine = newSigmaFunction({start = 1}, function(n, x)
    return (MATH.power(-1, n - 1) / MATH.factorial((2 * n) - 1)) * MATH.power(x, (2 * n) - 1)
end)

print(MATH.sine(5))