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By using certain operational techniques, the authors prove an elegant unification of several extensions of the well-known Mehler formula for Hermite polynomials, given recently by L. Carlitz (,  ). It is also shown how rapidly a number of Carlitz's formulas would follow from these considerations. The last section discusses a generalization involving the product of several Hermite polynomials of different arguments.doi:10.2307/2038530 fatcat:y3cgdgluzrc6pcq3fidkjjiuam