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On \(\lambda \)-Changhee-Hermite polynomials. (English) Zbl 1487.11029

Summary: In this paper, we introduce a new class of \(\lambda \)-analogues of the Changhee-Hermite polynomials and generalized Gould-Hopper-Appell type \(\lambda \)-Changhee polynomials, and present some properties and identities of these polynomials. A new class of polynomials generalizing different classes of Hermite polynomials such as the real Gould-Hopper, as well as the 1D and 2D holomorphic, ternary and polyanalytic complex Hermite polynomials and their relationship to the Appell type \(\lambda \)-Changhee polynomials are also discussed.

MSC:

11B83 Special sequences and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
05A30 \(q\)-calculus and related topics
05A40 Umbral calculus
11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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