  We build on a recent paper on Fourier expansions for the Riemann zeta
function. We establish Fourier expansions for certain $L$-functions, and offer
series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for
the coefficients. Fourier expansions for the reciprocal of the Riemann zeta
function are also stated. A new expansion for the Riemann xi function is
presented in the third section by constructing an integral formula using Mellin
transforms for its Fourier coefficients.
