On the coefficients of the polynomial iinduced by recyprocal roots revisited

Consider a polynomial P with complex coefficients and nonzero roots.What is the relation between the coefficients of P , and those of the polynomial P whose roots are reciprocal of the roots of P ?Is it possible to express the coefficients of P through a formula which depends on the coefficients of P ?The purpose of this note is to revisit this problem and respond affirmatively to these questions.Some examples will be provided for illustration purposes and as a motivation for this communication.