Some identities of degenerate Fubini polynomials arising from differential equations
Volume 11, Issue 3, pp 383--393
http://dx.doi.org/10.22436/jnsa.011.03.07
Publication Date: February 16, 2018
Submission Date: December 25, 2017
Revision Date: January 17, 2018
Accteptance Date: January 20, 2018
-
2163
Downloads
-
4168
Views
Authors
Sung-Soo Pyo
- Department of Mathematics Education, Silla University, Busan, Republic of Korea, Busan, Republic of Korea.
Abstract
Recently, Kim et al. have studied degenerate Fubini polynomials
in [T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 2857--2864]. Jang and Kim presented some identities of Fubini polynomials
arising from differential equations in [G.-W. Jang, T. Kim, Adv. Studies Contem. Math.,
\({\bf 28}\) (2018), to appear]. In this paper,
we drive differential equations from the generating function of the
degenerate Fubini polynomials. In addition, we obtain some
identities from those differential equations.
Share and Cite
ISRP Style
Sung-Soo Pyo, Some identities of degenerate Fubini polynomials arising from differential equations, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 3, 383--393
AMA Style
Pyo Sung-Soo, Some identities of degenerate Fubini polynomials arising from differential equations. J. Nonlinear Sci. Appl. (2018); 11(3):383--393
Chicago/Turabian Style
Pyo, Sung-Soo. "Some identities of degenerate Fubini polynomials arising from differential equations." Journal of Nonlinear Sciences and Applications, 11, no. 3 (2018): 383--393
Keywords
- Differential equations
- Fubini polynomials
- degenerate Fubini polynomials
MSC
References
-
[1]
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51–88
-
[2]
J.-M. De Koninck, Those Fascinating Numbers, American Mathematical Society, Providence (2009)
-
[3]
G.-W. Jang, T. Kim, Some identities of Fubini polynomials arising from differential equations, Adv. Studies Contem. Math., 28 (2018),
-
[4]
T. Kim, Identities involving Frobenius-Euler polynomials arising from non-linear differential equations, J. Number Theory, 132 (2012), 2854–2865
-
[5]
T. Kim, λ-analogue of Stirling numbers of the first kind, Adv. Stud. Contemp. Math., Kyungshang, 27 (2017), 423–429
-
[6]
T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, Differential equations for Changhee polynomials and their applications, J. Nonlinear Sci. Appl., 9 (2016), 2857–2864
-
[7]
D. S. Kim, T. Kim, Some identities for Bernoulli numbers of the second kind arising from a nonlinear differential equation, Bull. Korean Math. Soc., 52 (2015), 2001–2010
-
[8]
T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
-
[9]
T. Kim, D. S. Kim, G.-W. Jang, A note on degenerate Fubini polynomials, Proc. Jangjeon. Math. Soc., 20 (2017), 521-531
-
[10]
T. Kim, D. S. Kim, L. C. Jang, H. I. Kwon, Differential equations associated with Mittag-Leffer polynomials, Glob. J. Pure Appl. Math., 12 (2016), 2839–2847
-
[11]
S. Kim, B. M. Kim, J. Kwon, Differential equations associated with Genocchi polynomials, Glob. J. Pure Appl. Math., 12 (2016), 4579–4585
-
[12]
T. Kim, D. S. Kim, J. J. Seo, Differential equations associated with degenerate Bell polynomials, Inter. J. Pure Appl. Math., 108 (2016), 551–559
-
[13]
T. Kim, J. J. Seo, Revisit nonlinear differential equations arising from the generating functions of degenerate Bernoulli numbers, Adv. Stud. Contemp. Math., 2016 (26), 401-406
-
[14]
H. I. Kwon, T. Kim, J. J. Seo, A note on Daehee numbers arising from differential equations, Glob. J. Pure Appl., 12 (2016), 2349–2354
-
[15]
D. Lim, Some identities of degenerate Genocchi polynomials, Bull. Korean Math. Soc., 53 (2016), 569–579
-
[16]
M. Muresan, G. Toader, A generalization of Fubini’s number, Studia Univ. Babeş-Bolyai Math. , 31 (1986), 60–65
-
[17]
N. Pippenger, The hypercube of resistors, asymptotic expansions, and preferential arrangements, Math. Mag., 83 (2010), 331–346
-
[18]
S.-S. Pyo, T. Kim, S.-H. Rim, Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear Differential equation, J. Nonlinear Sci. Appl., 10 (2017), 6219–6228
-
[19]
S.-S. Pyo, Degenerate Cauchy numbers and polynomials of the fourth kind, Adv. Studies. Contemp. Math., 2018 (28),
-
[20]
S.-S. Pyo, T. Kim, S.-H. Rim, Degenerate Cauchy numbers of the third kind, preprint, (2018),
-
[21]
D. J. Velleman, G. S. Call, Permutations and combination locks, Math. Mag., 68 (1995), 243–253