The x-axis is the modified linear limb darkening coefficient x₁ = u₁ + β₁, the y-axis is the modified quadratic limb darkening coefficients x₂ = u₂ + β₂. u₁, u₂ are fixed. The point in the middle shows the u₁ = 0.41, u₂ = 0.25 point, i.e. the original value of the limb darkening coefficients of the example presented in Sect. 8. Contours represent the quantity ϵ_max, i.e. the absolute value of the maximum deviation of the original limb darkening function with u_1,2 coefficients from the limb darkening function with x_1,2 (δ run between 0 and 1).