In fact, this is correct, as can be demonstrated by directly calculating the Fourier coefficient from an integral:

Clearly, the (discrete infinite) set of Fourier coefficients and are variables defining the vector potential.

In applications, it is often useful to know the size of the Fourier coefficient.

Ask: does this means that they are the Fourier coefficients of the function?

A multi-dimensional integral is required to evaluate for calculating the Fourier coefficients.

The Fourier coefficients of can be looked up in a table, getting .

This is true when the negative Fourier coefficients of f all vanish.

The amplitude and phase of a sinusoid can be combined into a single complex number, called a Fourier coefficient.

The notation c is inadequate for discussing the Fourier coefficients of several different functions.

Each quantity was represented by a collection of Fourier coefficients with two indices, corresponding to the initial and final states.