# Differential equations for Daehee polynomials and their applications

Volume 10, Issue 4, pp 1303--1315
Publication Date: April 20, 2017 Submission Date: January 13, 2017
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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.

•  05A19
•  11B83
•  34A30

### References

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