david.jl

m = 2
n = 4*m + 1

a(j) = (1/n)*(1 + sin((2*π*j*m + π*j)/n)/sin((π*j)/n))

function b(j)
    s = 2
    for k = 1:m
        s += 2*cos((2*π*k*j)/n)
    end
    return s/n
end

# println(a(1) - a(2) + a(3) - a(4) + a(5))
# println(b(1) - b(2) + b(3) - b(4) + b(5))

a = 0
b = 0

for j = 1:n
    a += (-1)^(j + 1)*a(j)
    b += (-1)^(j + 1)*b(j)
    println(a)
    println(b)
end

println(a)
println(b)