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Certain Extensions of the Mehler Formula
Published online by Cambridge University Press: 20 November 2018
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For the Hermite polynomials Hn(z) defined by
1
it is easy to see from the Rodrigues formula that
2
where, as usual, Dz=d/dz.
In recent papers ([1], [2]) Carlitz has proved the following formulae:
3
4
where, 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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- Copyright © Canadian Mathematical Society 1972