  Starting from one-range addition theorems for Slater-type functions, which
are expansion in terms of complete and orthonormal functions based on the
generalized Laguerre polynomials, Guseinov constructed addition theorems that
are expansions in terms of Slater-type functions with a common scaling
parameter and integral principal quantum numbers. This was accomplished by
expressing the complete and orthonormal Laguerre-type functions as finite
linear combinations of Slater-type functions and by rearranging the order of
the nested summations. Essentially, this corresponds to the transformation of a
Laguerre expansion, which in general only converges in the mean, to a power
series, which converges pointwise. Such a transformation is not necessarily
legitimate, and this contribution discusses in detail the difference between
truncated expansions and the infinite series that result in the absence of
truncation
