  We give iterative constructions for irreducible polynomials over F_q of
degree nt^r for all nonnegative integers r, starting from irreducible
polynomials of degree n. The iterative constructions correspond modulo
fractional linear transformations to compositions with power functions x^t. The
R-transform introduced by Cohen is recovered as a particular case corresponding
to x^2, hence we obtain a generalization of Cohen's R-transform (t=2) to
arbitrary degrees t bigger that two. Important properties like self-reciprocity
and invariance of roots under certain automorphisms are deduced from invariance
under multiplication by appropriate roots of unity. Extending to quadratic
extensions of F_q we recover and generalize a recently obtained recursive
construction of Panario, Reis and Wang.
