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A note on λ-bernoulli numbers of the second kind
- Issue Date
- 2020
- Publisher
- Jangjeon Research Institute for Mathematical Sciences and Physics
- Keywords
- Degenerate cosine-Bernoulli polynomials; Degenerate cosine-Euler polynomials; Degenerate cosine-polynomials; Degenerate sine-Bemoulli polynomials; Degenerate sine-Euler polynomials; Degenerate sine-polynomials
- Citation
- Advanced Studies in Contemporary Mathematics (Kyungshang), v.30, no.2, pp.187 - 195
- Indexed
- SCOPUS
KCI
- Volume
- 30
- Number
- 2
- Start Page
- 187
- End Page
- 195
- ISSN
- 1229-3067
- Abstract
- In this paper, we study the λ-Bemoulli numbers of the second kind which are defined as an integral of the λ-analogue of the falling factorial sequence and express diem in terms of the λ-Stirling numbers of the first kind. Then we investigate the generalized λ-Bernoulli numbers of the second kind given as a multiple integral on the unit cube and show, among other things, the generating function of those numbers can be expressed in term of the recently introduced poly-exponential function by Kim-Kim. Finally, we introduce the higher-order λ-Bernoulli numbers of the second kind, again given by another multiple integral on the unit cube, and show those numbers can be given by the degenerate Stirling numbers of the second. ? 2020 Jangjeon Mathematical Society. All rights reserved.
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