Two properties of the Thiele reciprocal derivative

Abstract

It is proved that the Thiele's reciprocal derivative of the $(2n-1)$-th order of polynomial $ p_n (z), n \geq 2, $ is equal zero, and that the Thiele's reciprocal derivative of $2n$-th order of rational function $ p_m (z) / q_n (z), m <n, $ is equal zero too