New formulas for normalizing photon-added (-subtracted) two-mode squeezed thermal states

For the first time, we derive the compact forms of normalization factors for photon-added (-subtracted) two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators (IWOP) technique. It is found that these two factors are related to the Jacobi polynomials. In addition, some new relationships for Jacobi polynomials are presented.