The first statement follows readily from Theorem 6.37 and Proposition 7.3 applied to the functions $f_{i}(z)=\left(\log(z-\lambda_{i})-\sum_{j=2}^{n+1}\frac{1}{j}\right)(z-\lambda_{i})^{n+1}/(n+1)!$. The second statement follows similarly from Proposition 7.15. ∎