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We introduce coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at nonzero temperature (T ^ 0), as a "random" (or "thermal" or "noisy") basis in Hilbert space. A resolution of the identity for these states is proven and is used to generalize the usual pure (T = 0) coherent state formalism to the mixed (T ^ 0) case. This new formalism for thermal coherent states is then further generalized to a broader class of so-called negative-binomial mixeddoi:10.1142/s0217979207043865 fatcat:umhkfl7bezh6tobuj4n3rlnccu