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Using the thermal field dynamics theory to convert the thermal state to a"pure" state in doubled Fock space, it is found that the average value ofe^{fa^{{\dag}}a} under squeezed thermal state (STS) is just the generatingfunction of Legendre polynomials, a remarkable result. Based on this point, thenormalization and photon-number distributions of m-photon added (or subtracted)STS are conviently obtained as the Legendre polynomials. This new concisemethod can be expanded to the entangled case.

New approach for normalization and photon-number distributions of photon-added (-subtracted) squeezed thermal states