continuedfraction(v, u; atol=0, rtol=sqrt(eps(typeof(real(v(1) / u(1)))))

Calculate the continued fraction until convergence against specified tolerance ∑ᵢ uᵢ/vᵢ = v(0) + u(1) / (v(1) + u(2) / (v(2) + u(3)/(v(3) + ...)))