A new approach to fully degenerate Bernoulli numbers and polynomials
Filomat, Tome 37 (2023) no. 7, p. 2269
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
In this paper, we consider the doubly indexed sequence a (r) λ (n, m), (n, m ≥ 0), defined by a recurrence relation and an initial sequence a (r) λ (0, m), (m ≥ 0). We derive with the help of some differential operator an explicit expression for a (r) λ (n, 0), in term of the degenerate r-Stirling numbers of the second kind and the initial sequence. We observe that a (r) λ (n, 0) = β n,λ (r), for a (r) λ (0, m) = 1 m+1 , and a (r) λ (n, 0) = E n,λ (r), for a (r) λ (0, m) = 1 2 m. Here β n,λ (x) and E n,λ (x) are the fully degenerate Bernoulli polynomials and the degenerate Euler polynomials, respectively.
Classification :
11B68, 11B73, 11B83
Keywords: fully degenerate Bernoulli polynomials, degenerate Euler polynomials, degenerate r-Stirling numbers of the second kind
Keywords: fully degenerate Bernoulli polynomials, degenerate Euler polynomials, degenerate r-Stirling numbers of the second kind
Taekyun Kim; San Kim. A new approach to fully degenerate Bernoulli numbers and polynomials. Filomat, Tome 37 (2023) no. 7, p. 2269 . doi: 10.2298/FIL2307269K
@article{10_2298_FIL2307269K,
author = {Taekyun Kim and San Kim},
title = {A new approach to fully degenerate {Bernoulli} numbers and polynomials},
journal = {Filomat},
pages = {2269 },
year = {2023},
volume = {37},
number = {7},
doi = {10.2298/FIL2307269K},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2307269K/}
}
Cité par Sources :