TY - JOUR AU - Pyo, Sung-Soo AU - Kim, Taekyun AU - Rim, Seog-Hoon PY - 2017 TI - Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation JO - Journal of Nonlinear Sciences and Applications SP - 6219--6228 VL - 10 IS - 12 AB - 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 \(r\). SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.12.08 DO - 10.22436/jnsa.010.12.08 ID - Pyo2017 ER - TY - JOUR TI - Extended Stirling and exponential numbers AU - L. Carlitz JO - Duke Math. J. PY - 1965 DA - 1965// VL - 32 ID - Carlitz1965 ER - TY - JOUR TI - Degenerate Stirling, Bernoulli and Eulerian numbers AU - L. Carlitz JO - Utilitas Math. PY - 1979 DA - 1979// VL - 15 ID - Carlitz1979 ER - TY - JOUR TI - Some identities of symmetry for the degenerate q-Bernoulli polynomials under symmetry group of degree n AU - D. V. Dolgy AU - T. Kim AU - L.-C. Jang AU - H.-I. Kwon AU - J. J. Seo JO - Glob. J. Pure Appl. Math. PY - 2016 DA - 2016// VL - 12 ID - Dolgy2016 ER - TY - JOUR TI - New results on higher-order Daehee and Bernoulli numbers and polynomials AU - B. S. El-Desouky AU - A. Mustafa JO - Adv. Difference Equ. PY - 2016 DA - 2016// VL - 2016 ID - El-Desouky2016 ER - TY - JOUR TI - Multiparameter Higher Order Daehee and Bernoulli Numbers and Polynomials AU - B. S. El-Desouky AU - A. Mustafa AU - F. M. Abdel-Moneim JO - Applied Math. PY - 2017 DA - 2017// VL - 2017 ID - El-Desouky2017 ER - TY - JOUR TI - Revisit of identities of Daehee numbers arising from nonlinear differential equations AU - G.-W. Jang AU - T. Kim JO - Proc. Jangjeon Math. Soc. PY - 2017 DA - 2017// VL - 20 ID - Jang2017 ER - TY - JOUR TI - Some identities of ordered Bell numbers arising from differential equation AU - G.-W. Jang AU - T. Kim JO - Adv. Stud. Contemp. Math. PY - 2017 DA - 2017// VL - 27 ID - Jang2017 ER - TY - JOUR TI - Some identities of degenerate Daehee numbers arising from nonlinear differential equation AU - G.-W. Jang AU - J. Kwon AU - J. G. Lee JO - Adv. Difference Equ. PY - 2017 DA - 2017// VL - 2017 ID - Jang2017 ER - TY - JOUR TI - Identities involving Frobenius-Euler polynomials arising from non-linear differential equations AU - T. Kim JO - J. Number Theory PY - 2012 DA - 2012// VL - 132 ID - Kim2012 ER - TY - JOUR TI - On the degenerate Cauchy numbers and polynomials AU - T. Kim JO - Proc. Jangjeon Math. Soc. PY - 2015 DA - 2015// VL - 18 ID - Kim2015 ER - TY - JOUR TI - Degenerate Cauchy numbers and polynomials of the second kind AU - T. Kim JO - Adv. Stud. Contemp. Math. PY - 2017 DA - 2017// VL - 27 ID - Kim2017 ER - TY - JOUR TI - Some identities for Bernoulli numbers of the second kind arising from a non-linear differential equation AU - D. S. Kim AU - T. Kim JO - Bull. Korean Math. Soc. PY - 2015 DA - 2015// VL - 52 ID - Kim2015 ER - TY - JOUR TI - A note on nonlinear Changhee differential equations AU - T. Kim AU - D. S. Kim JO - Russ. J. Math. Phys. PY - 2016 DA - 2016// VL - 23 ID - Kim2016 ER - TY - JOUR TI - A note on degenerate Eulerian numbers and polynomials AU - D. S. Kim AU - T. Kim JO - Adv. Stud. Contemp. Math. PY - 2017 DA - 2017// VL - 27 ID - Kim2017 ER - TY - JOUR TI - On degenerate Bell numbers and polynomials AU - D. S. Kim AU - T. Kim JO - Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. PY - 2017 DA - 2017// VL - 111 ID - Kim2017 ER - TY - JOUR TI - A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on \(\mathbb{Z}_p\) AU - D. S. Kim AU - T. Kim AU - D. V. Dolgy JO - Appl. Math. Comput. PY - 2015 DA - 2015// VL - 259 ID - Kim2015 ER - TY - JOUR TI - Some identities of partially degenerate Touchard polynomials arising from differential equations AU - D. S. Kim AU - T. Kim AU - G. -W. Jang JO - Adv. Stud. Contemp. Math. PY - 2017 DA - 2017// VL - 27 ID - Kim2017 ER - TY - JOUR TI - Some identities of Laguerre polynomials arising from differential equations AU - T. Kim AU - D. S. Kim AU - K.-W. Hwang AU - J. J. Seo JO - Adv. Difference Equ. PY - 2016 DA - 2016// VL - 2016 ID - Kim2016 ER - TY - JOUR TI - Higher-order Cauchy Numbers and Polynomials AU - T. Kim AU - D. S. Kim AU - H. I. Kwon AU - J. J. Seo JO - Appl. Math. Sci. PY - 2015 DA - 2015// VL - 9 ID - Kim2015 ER - TY - JOUR TI - Differential equations arising from the generating function of general modified degenerate Euler numbers AU - T. Kim AU - D. S. Kim AU - H. I. Kwon AU - J. J. Seo JO - Adv. Difference Equ. PY - 2016 DA - 2016// VL - 2016 ID - Kim2016 ER - TY - JOUR TI - Revisit nonlinear differential equations associated with Bernoulli numbers of the second kind AU - T. Kim AU - D. S. Kim AU - H. I. Kwon AU - J. J. Seo JO - Glob. J. Pure Appl. Math. PY - 2016 DA - 2016// VL - 12 ID - Kim2016 ER - TY - JOUR TI - Linear differential equations for families of polynomials AU - T. Kim AU - D. S. Kim AU - T. Mansour AU - J. J. Seo JO - J. Inequal. Appl. PY - 2016 DA - 2016// VL - 2016 ID - Kim2016 ER - TY - JOUR TI - A note on the Degenerate High order Daehee polynomials AU - J.-W. Park AU - J. Kwon JO - Appl. Math. Sic. PY - 2015 DA - 2015// VL - 9 ID - Park2015 ER - TY - JOUR TI - Some identities on the Higher-order Daehee and Changhee Numbers AU - N. L. Wang AU - H. Li JO - Pure Appl. Math. J. PY - 2015 DA - 2015// VL - 4 ID - Wang2015 ER -