Araştırma Makalesi

Several recursive and closed-form formulas for some specific values of partial Bell polynomials

Cilt: 6 Sayı: 4 30 Aralık 2022
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EN

Several recursive and closed-form formulas for some specific values of partial Bell polynomials

Öz

In this paper, the authors derive several recursive and closed-form formulas for some specific values of partial Bell polynomials.

Anahtar Kelimeler

Kaynakça

  1. [1] T. Amdeberhan, X. Guan, L. Jiu, V.H. Moll, and C. Vignat, A series involving Catalan numbers: Proofs and demonstra- tions, Elem. Math. 71 (2016), no. 3, 109-121; available online at https://doi.org/10.4171/EM/306.
  2. [2] C.A. Charalambides, Enumerative Combinatorics, CRC Press Series on Discrete Mathematics and its Applications, Chap- man & Hall/CRC, Boca Raton, FL, 2002.
  3. [3] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Revised and Enlarged Edition, D. Reidel Publishing Co., 1974; available online at https://doi.org/10.1007/978-94-010-2196-8.
  4. [4] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Translated from the Russian, Translation edited and with a preface by Daniel Zwillinger and Victor Moll, Eighth edition, Revised from the seventh edition, Else- vier/Academic Press, Amsterdam, 2015; available online at https://doi.org/10.1016/B978-0-12-384933-5.00013-8.
  5. [5] B.-N. Guo, D. Lim, and F. Qi, Maclaurin's series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function, Appl. Anal. Discrete Math. 17 (2023), no. 1, in press; available online at https://doi.org/10.2298/ AADM210401017G.
  6. [6] B.-N. Guo, D. Lim, and F. Qi, Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions, AIMS Math. 6 (2021), no. 7, 7494-7517; available online at https://doi.org/10.3934/math.2021438.
  7. [7] Y. Hong, B.-N. Guo, and F. Qi, Determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind, CMES Comput. Model. Eng. Sci. 129 (2021), no. 1, 409?423; available online at https://doi.org/10.32604/cmes.2021.016431.
  8. [8] S. Jin, B.-N. Guo, and F. Qi, Partial Bell polynomials, falling and rising factorials, Stirling numbers, and combinatorial identities, CMES Comput. Model. Eng. Sci. 132 (2022), no. 3, 781-799; available online at https://dx.doi.org/10. 32604/cmes.2022.019941.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

30 Aralık 2022

Gönderilme Tarihi

5 Eylül 2022

Kabul Tarihi

29 Eylül 2022

Yayımlandığı Sayı

Yıl 2022 Cilt: 6 Sayı: 4

Kaynak Göster

APA
Du, W.- shih, Lım, D., & Qi, F. (2022). Several recursive and closed-form formulas for some specific values of partial Bell polynomials. Advances in the Theory of Nonlinear Analysis and its Application, 6(4), 528-537. https://doi.org/10.31197/atnaa.1170948
AMA
1.Du W shih, Lım D, Qi F. Several recursive and closed-form formulas for some specific values of partial Bell polynomials. ATNAA. 2022;6(4):528-537. doi:10.31197/atnaa.1170948
Chicago
Du, Wei-shih, Dongkyu Lım, ve Feng Qi. 2022. “Several recursive and closed-form formulas for some specific values of partial Bell polynomials”. Advances in the Theory of Nonlinear Analysis and its Application 6 (4): 528-37. https://doi.org/10.31197/atnaa.1170948.
EndNote
Du W- shih, Lım D, Qi F (01 Aralık 2022) Several recursive and closed-form formulas for some specific values of partial Bell polynomials. Advances in the Theory of Nonlinear Analysis and its Application 6 4 528–537.
IEEE
[1]W.- shih Du, D. Lım, ve F. Qi, “Several recursive and closed-form formulas for some specific values of partial Bell polynomials”, ATNAA, c. 6, sy 4, ss. 528–537, Ara. 2022, doi: 10.31197/atnaa.1170948.
ISNAD
Du, Wei-shih - Lım, Dongkyu - Qi, Feng. “Several recursive and closed-form formulas for some specific values of partial Bell polynomials”. Advances in the Theory of Nonlinear Analysis and its Application 6/4 (01 Aralık 2022): 528-537. https://doi.org/10.31197/atnaa.1170948.
JAMA
1.Du W- shih, Lım D, Qi F. Several recursive and closed-form formulas for some specific values of partial Bell polynomials. ATNAA. 2022;6:528–537.
MLA
Du, Wei-shih, vd. “Several recursive and closed-form formulas for some specific values of partial Bell polynomials”. Advances in the Theory of Nonlinear Analysis and its Application, c. 6, sy 4, Aralık 2022, ss. 528-37, doi:10.31197/atnaa.1170948.
Vancouver
1.Wei-shih Du, Dongkyu Lım, Feng Qi. Several recursive and closed-form formulas for some specific values of partial Bell polynomials. ATNAA. 01 Aralık 2022;6(4):528-37. doi:10.31197/atnaa.1170948

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