Geodesic
Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation
Pyo, Sung-Soo 1 ; Kim, Taekyun 2 ; Rim, Seog-Hoon 3
1 Department of Mathematics Education, Silla University, Busan, Rep. of Korea
2 Department of Mathematics, Kwangwoon University, Seoul, Rep. of Korea
3 Department of Mathematics Education, Kyungpook National University, Taegu, Rep. of Korea
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 12, p. 6219-6228.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, Glob. J. Pure Appl. Math., ${\bf 12}$ (2016), 1893--1901], Kim et al. presented some identities for the Bernoulli numbers of the second kind using differential equation. Here we use this differential equation in a different way. In this paper, we deduce some identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind of order $r$.
DOI : 10.22436/jnsa.010.12.08
Classification : 05A19, 11B37, 11B83, 34A34
Keywords: Degenerate Daehee numbers, Bernoulli numbers of the second kind, nonlinear differential equation

Pyo, Sung-Soo  1 ; Kim, Taekyun  2 ; Rim, Seog-Hoon  3

1 Department of Mathematics Education, Silla University, Busan, Rep. of Korea
2 Department of Mathematics, Kwangwoon University, Seoul, Rep. of Korea
3 Department of Mathematics Education, Kyungpook National University, Taegu, Rep. of Korea 
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Pyo, Sung-Soo ; Kim, Taekyun ; Rim, Seog-Hoon . Identities of the degenerate Daehee numbers  with the Bernoulli numbers of the second kind arising from nonlinear differential equation. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 12, p. 6219-6228. doi : 10.22436/jnsa.010.12.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.12.08/

[1] Carlitz, L. Extended Stirling and exponential numbers, Duke Math. J., Volume 32 (1965), pp. 205-224

[2] Carlitz, L. Degenerate Stirling, Bernoulli and Eulerian numbers , Utilitas Math., Volume 15 (1979), pp. 51-88 | Zbl

[3] Dolgy, D. V.; Kim, T.; Jang, L.-C.; Kwon, H.-I.; Seo, J. J. Some identities of symmetry for the degenerate q-Bernoulli polynomials under symmetry group of degree n, Glob. J. Pure Appl. Math., Volume 12 (2016), pp. 4385-4394

[4] El-Desouky, B. S.; Mustafa, A. New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Difference Equ., Volume 2016 (2016), pp. 1-21 | DOI

[5] El-Desouky, B. S.; Mustafa, A.; Abdel-Moneim, F. M. Multiparameter Higher Order Daehee and Bernoulli Numbers and Polynomials, Applied Math., Volume 2017 (2017), pp. 775-785 | DOI

[6] Jang, G.-W.; Kim, T. Revisit of identities of Daehee numbers arising from nonlinear differential equations , Proc. Jangjeon Math. Soc., Volume 20 (2017), pp. 163-177 | Zbl | DOI

[7] Jang, G.-W.; Kim, T. Some identities of ordered Bell numbers arising from differential equation, Adv. Stud. Contemp. Math., Volume 27 (2017), pp. 385-397 | Zbl

[8] Jang, G.-W.; Kwon, J.; J. G. Lee Some identities of degenerate Daehee numbers arising from nonlinear differential equation, Adv. Difference Equ., Volume 2017 (2017), pp. 1-10 | DOI

[9] Kim, T. Identities involving Frobenius-Euler polynomials arising from non-linear differential equations, J. Number Theory, Volume 132 (2012), pp. 2854-2865 | Zbl | DOI

[10] Kim, T. On the degenerate Cauchy numbers and polynomials, Proc. Jangjeon Math. Soc., Volume 18 (2015), pp. 307-312 | Zbl

[11] Kim, T. Degenerate Cauchy numbers and polynomials of the second kind, Adv. Stud. Contemp. Math., Volume 27 (2017), pp. 441-449 | DOI | Zbl

[12] Kim, D. S.; Kim, T. Some identities for Bernoulli numbers of the second kind arising from a non-linear differential equation, Bull. Korean Math. Soc., Volume 52 (2015), pp. 2001-2010 | Zbl | DOI

[13] Kim, T.; Kim, D. S. A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., Volume 23 (2016), pp. 88-92 | Zbl | DOI

[14] Kim, D. S.; T. Kim A note on degenerate Eulerian numbers and polynomials, Adv. Stud. Contemp. Math., Volume 27 (2017), pp. 431-440 | DOI | Zbl

[15] Kim, D. S.; Kim, T. On degenerate Bell numbers and polynomials, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., Volume 111 (2017), pp. 435-446 | Zbl | DOI

[16] Kim, D. S.; Kim, T.; D. V. Dolgy A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on \(\mathbb{Z}_p\), Appl. Math. Comput., Volume 259 (2015), pp. 198-204 | DOI

[17] Kim, D. S.; Kim, T.; Jang, G. -W. Some identities of partially degenerate Touchard polynomials arising from differential equations, Adv. Stud. Contemp. Math., Volume 27 (2017), pp. 243-251 | Zbl | DOI

[18] Kim, T.; Kim, D. S.; Hwang, K.-W.; Seo, J. J. Some identities of Laguerre polynomials arising from differential equations , Adv. Difference Equ., Volume 2016 (2016), pp. 1-9 | DOI

[19] Kim, T.; Kim, D. S.; Kwon, H. I.; Seo, J. J. Higher-order Cauchy Numbers and Polynomials, Appl. Math. Sci., Volume 9 (2015), pp. 1989-2004

[20] Kim, T.; Kim, D. S.; Kwon, H. I.; Seo, J. J. Differential equations arising from the generating function of general modified degenerate Euler numbers, Adv. Difference Equ., Volume 2016 (2016), pp. 1-7 | DOI

[21] Kim, T.; Kim, D. S.; Kwon, H. I.; Seo, J. J. Revisit nonlinear differential equations associated with Bernoulli numbers of the second kind, Glob. J. Pure Appl. Math., Volume 12 (2016), pp. 1893-1901

[22] Kim, T.; Kim, D. S.; Mansour, T.; Seo, J. J. Linear differential equations for families of polynomials, J. Inequal. Appl., Volume 2016 (2016), pp. 1-8 | DOI

[23] Park, J.-W.; Kwon, J. A note on the Degenerate High order Daehee polynomials, Appl. Math. Sic., Volume 9 (2015), pp. 4635-4642

[24] Wang, N. L.; Li, H. Some identities on the Higher-order Daehee and Changhee Numbers , Pure Appl. Math. J., Volume 4 (2015), pp. 33-37

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