# Representation of the three-body Coulomb Green's function in parabolic coordinates: paths of integration

## TL;DR

This paper investigates the use of straight-line integration paths for computing the three-body Coulomb Green's function, demonstrating that only specific contours yield valid integral representations.

## Contribution

It identifies the correct straight-line integration contour for the three-body Coulomb Green's function, clarifying a key aspect of its integral representation.

## Key findings

- Only one straight-line path yields a valid integral representation
- Numerical examples confirm the validity of the specific contour
- Clarifies the conditions for valid integral paths in three-body Coulomb problems

## Abstract

The possibility is discussed of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function. In our numerical examples two different integration contours are considered. It is demonstrated that only one of these straight-line paths provides that the integral representation is valid.