Abstract
For the Hermite polynomials Hn(z) defined by1it is easy to see from the Rodrigues formula that2where, as usual, Dz=d/dz.In recent papers ([1], [2]) Carlitz has proved the following formulae:34where, on the right-hand side of (4), the range of each summation is from i= 1 to i=k(k=1,2,…).
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