  Frobenius observed that the number of times an element of a finite group is
obtained as a commutator is given by a specific combination of the irreducible
characters of the group. More generally, for any word w the number of times an
element is obtained by substitution in w is a class function. Thus, it has a
presentation as a combination of irreducible characters, called its Fourier
expansion. In this paper we present formulas regarding the Fourier expansion of
words in which some letters appear twice. These formulas give simple proofs for
classical results, as well as new ones.
