  We study the expansions of the completed Riemann zeta function and completed
Dirichlet L-functions in Meixner-Pollaczek polynomials. We give the proof of
the uniform convergence, the multiplicative structure for the coefficients of
these expansions, and a calculation for the coefficients of a completed
Dirichlet L-function $\hat{L}(s, \chi_{-1})$. Furthermore, we give a boundary
for the zeros of the approximating polynomial.
