A series solution for the \(GV\psi_ 0\) term of the Born series (Q1805274)

A series representation for the function \(B(k, r):= \frac{i} {2k} \int_{-\infty}^\infty e^{ik|r- r'|} V(r') e^{ik r'} d r'\) is presented, where \(V\) arises as a potential in the differential equation (1) \((\frac{\partial^2} {\partial r^2}+ k^2)\psi (k, r)= V(r)\psi(k, r)\). The function \(B\) represents the second term of the Born series giving the general solution to (1).