### Degenerate Sheffer sequences and lambda-Sheffer sequences

- 주제(키워드) 도움말 Umbral calculus , Degenerate Sheffer sequence , lambda-Linear functional , lambda-Differential operator , lambda-Sheffer operator , lambda-Umbral operator
- 발행기관 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행년도 2021
- 총서유형 Journal
- 본문언어 영어

#### 초록/요약 도움말

In the 1970s, Gian-Carlo Rota laid a rigorous foundation for umbral calculus which is based on the modern concepts like a linear functional, a differential operator and an adjoint. The motivation for this paper starts from the question that what if the usual exponential function in the generating function of a Sheffer sequence is replaced by degenerate exponential functions. The sequences thus defined are called lambda-Sheffer sequences. It may be said that this question is very natural in view of the regained recent interests in degenerate special numbers and polynomials. It turns out that these correspond to replacing the linear functional and the differential operator respectively by lambda-linear functionals and lambda-differential operators. In this article, we give an account of lambda-Sheffer sequences and degenerate Sheffer sequences, and illustrate them with many examples. (c) 2020 Elsevier Inc. All rights reserved.

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