  This article is a thorough critique to the Weniger's comments made to our
papers published in prestigious journals in the recent years. A detailed and
critical examination of the arguments that led to the suggested comment by
Weniger reveals some serious flaws. In our published papers we have shown that
the unsymmetrical and symmetrical one-range addition theorems for Slater type
orbitals, Coulomb-Yukawa like correlated interaction potentials (CIPs) and
their derivatives are derived from the expansions in terms of -ETOs that are
complete and orthonormal sets of exponential type orbitals in corresponding
Hilbert spaces, where The concrete criticism raised in Weniger's comment
against our papers actually touches a very minor aspect of the works that are
not relevant at all for the conclusions, which are made. As can be seen from
our papers, all of the formulas for different kinds of multicenter integrals
over Slater type orbitals with integer and noninteger principal quantum numbers
obtained by the use of unsymmetrical and symmetrical one-range addition
theorems were tested by computer calculations. We reject the Weniger's personal
views about papers published by Guseinov and his coworkers from 1978 to 2006
and respectable referees on one-range addition theorems and multicenter
integrals. All claims of inconsistencies and flaws in the theoretical framework
are rejected as unfounded. This rejoinder paper contains all of the answers to
Weniger's comments.
