  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 of
e^{fa^{{\dag}}a} under squeezed thermal state (STS) is just the generating
function of Legendre polynomials, a remarkable result. Based on this point, the
normalization and photon-number distributions of m-photon added (or subtracted)
STS are conviently obtained as the Legendre polynomials. This new concise
method can be expanded to the entangled case.
