  A series of the form
$\sum_{\ell=0}^{\infty}c(\kappa,\ell)\,M_{\kappa,\ell+1/2}(r_{0})W_{\kappa,\ell+1/2}(r)P_{\ell}(\cos(\gamma))$
is evaluated explicitly where $c(\kappa,\ell)$ are suitable complex
coefficients, $M_{\kappa,\mu}$ and $W_{\kappa,\mu}$ are the Whittaker
functions, $P_{\ell}$ are the Legendre polynomials, $r_{0}<r$ are radial
variables, $\gamma$ is an angle and $\kappa$ is a complex parameter. The sum
depends, as far as the radial variables and the angle are concerned, on their
combinations $r+r_{0}$ and $(r^{2}+r_{0}^{\,2}-rr_{0}\cos(\gamma))^{1/2}$. This
addition formula generalizes in some respect Gegenbauer's Addition Theorem and
follows rather straightforwardly from some already known results, particularly
from Hostler's formula for Coulomb Green's function. In addition, several
complementary summation formulas are derived. They suggest that a further
extension of this addition formula may be possible.
