Journals / Mathematical Sciences and Applications E-Notes / 2019 / Cilt: 7 - Sayı: 2

Relations Among Bell Polynomials, Central Factorial Numbers, and Central Bell Polynomials

Pages
191–194
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In the note, by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of thesecond kind, the authors derive three relations among the Bell polynomials, central factorial numbers ofthe second kind, and central Bell polynomials.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the note, by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of thesecond kind, the authors derive three relations among the Bell polynomials, central factorial numbers ofthe second kind, and central Bell polynomials.
📊
Key Findings & Data:In the note, by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of thesecond kind, the authors derive three relations among the Bell polynomials, central factorial numbers ofthe second kind, and central Bell polynomials.
💡
Conclusion & Impact:In the note, by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of thesecond kind, the authors derive three relations among the Bell polynomials, central factorial numbers ofthe second kind, and central Bell polynomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the note, by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of thesecond kind, the authors derive three relations among the Bell polynomials, central factorial numbers ofthe second kind, and central Bell polynomials.

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Cite This Article

QI, F., GUO, B. (2022). Relations Among Bell Polynomials, Central Factorial Numbers, and Central Bell Polynomials. Mathematical Sciences and Applications E-Notes, Cilt: 7 - Sayı: 2, 191–194. https://ajindex.com/articles/578850

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References (13)

  1. Butzer, P. L., Schmidt, M., Stark, E. L. and Vogt, L., Central factorial numbers; their main properties and some applications, Numer. Funct. Anal. Optim. 10 (1989), no. 5-6, 419–488; available online at https://doi.org/ 10.1080/01630568908816313
  2. Charalambides, C. A., Enumerative Combinatorics, CRC Press Series on Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton, FL, 2002
  3. Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions, Revised and Enlarged Edition, D. Reidel Publishing Co., 1974; available online at
  4. Guo, B.N. and Qi, F., An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions, Glob. J. Math. Anal. 2 (2014), no. 4, 243–248; available online at http://dx.doi.org/10.14419/gjma. v2i4.3310
  5. Kim, D. S., Jang, G.W., Dolgy, D. V. and Kim, T., An expression for central Bell polynomials, Adv. Stud. Contemp. Math. 29 (2019), no. 2, 257–262; available online at
  6. Merca, M., Connections between central factorial numbers and Bernoulli polynomials, Period. Math. Hungar. 73 (2016), no. 2, 259–264; available online at
  7. Qi, F., An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers, Mediterr. J. Math. 13 (2016), no. 5, 2795–2800; available online at
  8. Qi, F., Integral representations for multivariate logarithmic polynomials, J. Comput. Appl. Math. 336 (2018), 54–62; available online at
  9. Qi, F., On multivariate logarithmic polynomials and their properties, Indag. Math. (N.S.) 29 (2018), no. 5, 1179–1192; available online at
  10. Qi, F., Simplifying coefficients in differential equations related to generating functions of reverse Bessel and partially degenerate Bell polynomials, Bol. Soc. Paran. Mat. 39 (2021), no. 4, in press; available online at http://dx.doi. org/10.5269/bspm.41758
  11. Qi, F., Some inequalities and an application of exponential polynomials, Math. Inequal. Appl. 22 (2019), in press; available online at
  12. Qi, F., Some inequalities for the Bell numbers, Proc. Indian Acad. Sci. Math. Sci. 127 (2017), no. 4, 551–564; available online at
  13. Qi, F., Cer ˇna