Erratum to "Solutions problem 89-2: On the principal value of a quadruple integral", SIAM Rev. 32 (1990) 143

TL;DR

This paper corrects a previous claim about a quadruple integral's value, showing the original problem remains unsolved due to overlooked symmetry issues in the prior solution.

Contribution

It identifies an error in W. B. Jordan's previous conclusion, clarifying that the quadruple integral's value does not vanish and the problem remains open.

Findings

Jordan's conclusion is invalid due to overlooked symmetry.

The quadruple integral does not vanish as previously claimed.

The original problem remains unsolved.

Abstract

W. B. Jordan's conclusion that the quadruple principal value integral in problem 89-2 vanishes does not hold. The error sneaks in through a contribution of a subintegral which impedes some sign symmetry with respect to the master parameter (the Fermi radius) and which was overlooked in the published solution. In summary, the original problem of solving the quadruple integral remains unsolved.