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In this paper, we reconsider some results by Nieto and Truax about generatingfunctions for arbitrary order coherent and squeezed states. These results wereobtained using the exponential of the Laplacian operator; more elaboratedoperational identities were used by Dattoli et al. \cite{Dattoli} to extendthese results. In this note, we show that the operational approach can bereplaced by a purely probabilistic approach, in the sense that the exponentialof derivatives operators can be identified with equivalent expectationoperators. This approach brings new insight about the kinks between operationaland probabilistic calculus.

A probabilistic approach to some results by Nieto and Truax