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Several formulas for Bernoulli numbers and polynomials
- Source :
- Advances in Mathematics of Communications. 17:522-535
- Publication Year :
- 2023
- Publisher :
- American Institute of Mathematical Sciences (AIMS), 2023.
-
Abstract
- A generalized Stirling numbers of the second kind \begin{document}$ S_{a,b}\left(p,k\right) $\end{document} , involved in the expansion \begin{document}$ \left(an+b\right)^{p} = \sum_{k = 0}^{p}k!S_{a,b}\left(p,k\right) \binom{n}{k} $\end{document} , where \begin{document}$ a \neq 0, b $\end{document} are complex numbers, have studied in [ 16 ]. In this paper, we show that Bernoulli polynomials \begin{document}$ B_{p}(x) $\end{document} can be written in terms of the numbers \begin{document}$ S_{1,x}\left(p,k\right) $\end{document} , and then use the known results for \begin{document}$ S_{1,x}\left(p,k\right) $\end{document} to obtain several new explicit formulas, recurrences and generalized recurrences for Bernoulli numbers and polynomials.
- Subjects :
- Algebra and Number Theory
Computer Networks and Communications
Applied Mathematics
020206 networking & telecommunications
Stirling numbers of the second kind
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Microbiology
Bernoulli polynomials
Combinatorics
symbols.namesake
010201 computation theory & mathematics
0202 electrical engineering, electronic engineering, information engineering
symbols
Discrete Mathematics and Combinatorics
Bernoulli number
Complex number
Mathematics
Subjects
Details
- ISSN :
- 19305338 and 19305346
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics of Communications
- Accession number :
- edsair.doi...........c9fe168cac6baab12724775223c5c3ce