We construct photon-subtracted(-added) thermo vacuum state by normalizing them.As their application we derive some new generating function formulas of Jacobi polynomials,which may be applied to study other problems in quantum mechanics. This will also stimulate the research of mathematical physics in the future.
We show that the two-mode photon-subtracted squeezed state (TPSSS) is a squeezed two-variable Hermite polynomial excitation state, and we can therefore determine its normalization as a Jacobi polynomial of the squeezing parameter. Some new relations about the Jacobi polynomials are obtained by this analysis. We also show that the TPSSS can be treated as a two-variable Hermite-polynomial excitation on squeezed vacuum state. The technique of integration within an ordered product of operators brings convenience in our derivation.