In the Appendix B of Yang, Wu & Ren (2021), we made the statement that the Green function $G$ has the symmetry property with respect to the field point $P(x_{1},y_{1},z_{1})$ and field point $P_{0}(x_{0},y_{0},z_{0})$ , or $G(x_{1},y_{1},z_{1};x_{0},y_{0},z_{0})=G(x_{0},y_{0},z_{0};x_{1},y_{1},z_{1})$ . This is not always correct.

The mistake arose from the statement below (B2) that ‘Although $G$ and $\xi$ involve only the real part, we may use the whole complex function here’. In the derivations followed, the full complex functions of $G_{i}$ and $\xi _{i}$ ( $i=0$ , 1) in (B1) and (B2) were directly used without taking their real parts, which led to an incorrect conclusion. However, it should be noted that when $0\lt Fn\lt Fn_{c}^{(1)}$ , $G_{i}$ and $\xi _{i}$ contain only the $k_{0}$ component. $G_{i}^{(0)}$ is fully real and $\xi _{i}^{(0)}$ is fully imaginary, and they can be taken out of the operator $\mathrm{Re}\{\, \}$ . Therefore, the symmetry property is satisfied within this range.

In summary, the symmetry property $G(x_{1},y_{1},z_{1};x_{0},y_{0},z_{0})=G(x_{0},y_{0},z_{0};$ $x_{1},y_{1},z_{1})$ holds only when $0\lt Fn\lt Fn_{c}^{(1)}$ , and it is incorrect when $Fn\gt Fn_{c}^{(1)}$ .

This mistake is confined solely to the Appendix B, and it does not affect any other formulas or results presented in the paper.