Representations of degenerate Hermite polynomials

28 Oct 2020  ·  Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee, Hanyoung Kim ·

We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer polynomials we represent the degenerate Hermite polynomials in terms of the higher-order degenerate Bernoulli, Euler, and Frobenius-Euler polynomials and vice versa.

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Number Theory 05A40, 11B68, 11B83