Abstract
The aim of this paper is to construct new generating functions for Hermite base Bernoulli type polynomials, which generalize not only the Milne-Thomson polynomials but also the two-variable Hermite polynomials. We also modify the Milne-Thomson polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. Moreover, by applying the umbral algebra to these generating functions, we derive new identities for the Bernoulli polynomials of higher order, the Hermite polynomials and numbers of higher order, and the Stirling numbers of the second kind.
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Dere, R., Simsek, Y. Hermite base Bernoulli type polynomials on the umbral algebra. Russ. J. Math. Phys. 22, 1–5 (2015). https://doi.org/10.1134/S106192081501001X
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DOI: https://doi.org/10.1134/S106192081501001X