Differential equations for Daehee polynomials and their applications
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Authors
Dongkyu Lim
- School of Mathematical Sciences, Nankai University, Tianjin Ciy, 300071, China.
Abstract
Recently, differential equations for Changhee polynomials and their applications were introduced by Kim et al. and by using
their differential equations, they derived some new identities on Changhee polynomials. Specially, they presented Changhee
polynomials \(Ch_{n+N}(x)\) by sums of lower terms of Changhee polynomials \(Ch_{n}(x)\). Compare to the result, Kim et al. described
Changhee polynomials \(Ch_{n+N}(x)\) via lower term of higher order Chaghee polynomials by using non-linear differential equations
arising from generating function of Changhee polynomials. In the first part of this paper, the author uses the idea of Kim et al.
to apply to generating function for Daehee polynomials. From differential equations associated with the generating function of
those polynomials, we derive some formulae and combinatorial identities.
Also, Kwon et al. developed the method of differential equations from the generating function of Daehee numbers and
investigated new explicit identities of Daehee numbers. In the second part of the present paper, the author applies their methods
to generating function of Daehee polynomials, and get the explicit representations of Daehee polynomials. And specially we
put \(x = 0\) in our results, we can get new representations of Daehee numbers compare to the above results.
Share and Cite
ISRP Style
Dongkyu Lim, Differential equations for Daehee polynomials and their applications, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1303--1315
AMA Style
Lim Dongkyu, Differential equations for Daehee polynomials and their applications. J. Nonlinear Sci. Appl. (2017); 10(4):1303--1315
Chicago/Turabian Style
Lim, Dongkyu. "Differential equations for Daehee polynomials and their applications." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1303--1315
Keywords
- Daehee polynomial
- Daehee number
- differential equations.
MSC
References
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