Reply to `Extended Rejoinder to "Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys. Vol. 309 (2005), pp. 209 - 211)", arXiv:0706.0975v2"

TL;DR

This paper addresses and clarifies mathematical issues in Guseinov's derivation of one-range addition theorems for Coulomb potentials, responding to critiques and defending the validity of Guseinov's work.

Contribution

The paper provides a detailed analysis of the mathematical flaws in Guseinov's treatment of addition theorems, clarifying misunderstandings and defending the original derivations.

Findings

Identifies and discusses serious mathematical flaws in Guseinov's approach.

Clarifies the validity of Guseinov's derivations of addition theorems.

Responds to critiques by Weniger and others, defending Guseinov's work.

Abstract

In the years from 2001 to 2006, Guseinov and his coworkers published 40 articles on the derivation and application of one-range addition theorems. In E. J. Weniger, Extended Comment on ``One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives'' by I. I. Guseinov (Chem. Phys. Vol. 309 (2005), pp. 209 - 213), arXiv:0704.1088v2 [math-ph], it was argued that Guseinov's treatment of one-range addition theorems is at best questionable and in some cases fundamentally flawed. In I. I. Guseinov, Extended Rejoinder to "Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives'' by I. I. Guseinov (Chem. Phys. and Vol. 309 (2005)'', pp. 209-213), arXiv:0706.0975v2 [physics.chem-ph], these claims were disputed. To clarify the situation, the most serious mathematical flaws in Guseinov's treatment of one-range addition theorems are discussed in more depth.