Reciprocal derivatives of the 2nd type and rational functions

Abstract

New properties of reciprocal derivatives of the 2nd type are studied. It
is proved that the reciprocal derivative of the 2nd type of the (2n)–th
order of the polynomials p n (z) is equal to zero, and that the reciprocal
derivative of the 2nd type of the (2n−1)–th order of the rational function
p m (z)/q n (z),m < n, is equal to zero as well.