Some identities of degenerate Daehee numbers arising from certain differential equations
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Authors
Taekyun Kim
- Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China.
- Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea.
Dae San Kim
- Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea.
Abstract
In this paper, we introduce the degenerate Daehee numbers and study a family of differential equations associated with
the generating function of these numbers. From those differential equations, we will be able to obtain some new and interesting
combinatorial identities involving the degenerate Daehee numbers and generalized harmonic numbers.
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ISRP Style
Taekyun Kim, Dae San Kim, Some identities of degenerate Daehee numbers arising from certain differential equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 744--751
AMA Style
Kim Taekyun, Kim Dae San, Some identities of degenerate Daehee numbers arising from certain differential equations. J. Nonlinear Sci. Appl. (2017); 10(2):744--751
Chicago/Turabian Style
Kim, Taekyun, Kim, Dae San. "Some identities of degenerate Daehee numbers arising from certain differential equations." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 744--751
Keywords
- Degenerate Daehee numbers
- differential equation
- generalized harmonic numbers.
MSC
References
-
[1]
A. Bayad, T. Kim, Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator, Russ. J. Math. Phys., 23 (2016), 164–171.
-
[2]
L. Carlitz, A degenerate Staudt-Clausen theorem, Arch. Math. (Basel), 7 (1956), 28–33.
-
[3]
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51–88.
-
[4]
D. V. Dolgy, D. S. Kim, T. Kim, On the Korobov polynomials of the first kind, (Russian) Mat. Sb., 208 (2017), 65–79.
-
[5]
D. V. Dolgy, D. S. Kim, T. Kim, T. Mansour, Degenerate poly-Bernoulli polynomials of the second kind, J. Comput. Anal. Appl., 21 (2016), 954–966.
-
[6]
B. S. El-Desouky, A. Mustafa, New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Difference Equ., 2016 (2016), 21 pages.
-
[7]
T. Kim, Identities involving Frobenius-Euler polynomials arising from non-linear differential equations, J. Number Theory, 132 (2012), 2854–2865.
-
[8]
D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969–5976.
-
[9]
D. S. Kim, T. Kim, A note on degenerate poly-Bernoulli numbers and polynomials, Adv. Difference Equ., 2015 (2015), 8 pages.
-
[10]
D. S. Kim, T. Kim, Identities arising from higher-order Daehee polynomial bases, Open Math., 13 (2015), 196–208.
-
[11]
D. S. Kim, T. Kim, Some identities for Bernoulli numbers of the second kind arising from a non-linear differential equation, Bull. Korean Math. Soc., 52 (2015), 2001–2010.
-
[12]
T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88–92.
-
[13]
T. Kim, D. S. Kim, K.-W. Hwang, J.-J. Seo, Some identities of Laguerre polynomials arising from differential equations, Adv. Difference Equ., 2016 (2016), 9 pages.
-
[14]
T. Kim, D. S. Kim, H. I. Kwon, D. V. Dolgy, J.-J. Seo, Degenerate falling factorial polynomials, Adv. Stud. Contemp. Math., 26 (2016), 481–499.
-
[15]
T. Kim, D. S. Kim, T. Mansour, J.-J. Seo, Linear differential equations for families of polynomials, J. Inequal. Appl., 2016 (2016 ), 8 pages.
-
[16]
N. M. Korobov , On some properties of special polynomials, (Russian) Proceedings of the IV International Conference ''Modern Problems of Number Theory and its Applications'' (Russian), Tula, (2001), Chebyshevskiı Sb., 1 (2001), 40–49.
-
[17]
H. I. Kwon, T. Kim, J.-J. Seo, A note on degenerate Changhee numbers and polynomials, Proc. Jangjeon Math. Soc., 18 (2015), 295–305.
-
[18]
J. G. Lee, L.-C. Jang, J.-J. Seo, S.-K. Choi, H. I. Kwon, On Appell-type Changhee polynomials and numbers, Adv. Difference Equ., 2016 (2016 ), 10 pages.
-
[19]
E.-J. Moon, J.-W. Park, S.-H. Rim, A note on the generalized q-Daehee numbers of higher order, Proc. Jangjeon Math. Soc., 17 (2014), 557–565.
-
[20]
H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math. (Kyungshang), 18 (2009), 41–48.
-
[21]
J.-J. Seo, S. H. Rim, T. Kim, S. H. Lee, Sums products of generalized Daehee numbers, Proc. Jangjeon Math. Soc., 17 (2014), 1–9.
-
[22]
Y. Simsek, Apostol type Daehee numbers and polynomials, Adv. Stud. Contemp. Math., 26 (2016), 555–566.
-
[23]
A. V. Ustinov, Korobov polynomials and umbral analysis, (Russian) Chebyshevskiı Sb., 4 (2003), 137–152.
-
[24]
N. L. Wang, H.-L. Li, Some identities on the higher-order Daehee and Changhee numbers, Pure Appl. Math. J., 4 (2015), 33–37.