A note on $lanbda$-Bernoulli numbers of the second kindA note on $lanbda$-Bernoulli numbers of the second kind
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- A note on $lanbda$-Bernoulli numbers of the second kind
- 김대산; 김태균; 권종겸; 이현석
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- degenerate cosine-Euler polynomials; degenerate sine-Euler polynomials; degenerate cosine-Bernoulli polynomials; degenerate sine-Bernoulli polynomials; degenerate cosine-polynomials; degenerate sine- polynomials
- Advanced Studies in Contemporary Mathematics, v.30, no.2, pp.187 - 196
- Journal Title
- Advanced Studies in Contemporary Mathematics
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- End Page
- In this paper, we study the λ -Bernoulli numbers of the second kind which are defined as an integral of the λ -analogue of the falling factorial sequence and express them 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.
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