Volume 4, Issue 5-1, October 2015, Page: 33-37
Some identities on the Higher-order Daehee and Changhee Numbers
Nian Liang Wang, Department of Applied Mathematics, Shangluo University, Shangluo, Peoples Republic of China
Hailong Li, Department of Mathematics and Information Science, Weinan Normal University, Weinan, Peoples Republic of China
Received: Jun. 1, 2015;       Accepted: Jun. 16, 2015;       Published: Aug. 5, 2015
DOI: 10.11648/j.pamj.s.2015040501.17      View  3530      Downloads  90
Abstract
In this note, we shall give an explicit formula for the coefficients of the expansion of given generating function, when that function has an appropriate form, the coefficients can be represented by the higher-order Daehee and Changhee polynomials and numbers of the first kind. By the classical method of comparing the coefficients of the generating function, we show some interesting identities related to the Higher-order Daehee and Changhee numbers.
Keywords
Higher-order Daehee Numbers, Higher-order Changhee Numbers, Bernoulli Number, Euler Number
To cite this article
Nian Liang Wang, Hailong Li, Some identities on the Higher-order Daehee and Changhee Numbers, Pure and Applied Mathematics Journal. Special Issue: Mathematical Aspects of Engineering Disciplines. Vol. 4, No. 5-1, 2015, pp. 33-37. doi: 10.11648/j.pamj.s.2015040501.17
Reference
[1]
D. S. Kim, T. Kim, S.-H. Lee, and J.-J. Seo, Higher-order Daehee numbers and polynomials, International Journal of Mathematical Analysis 8 (2014), no. 5-6,273–283.
[2]
D. S. Kim, T. Kim, and J.-J. Seo, Higher-order Daehee polynomials of the first kind with umbral calculus, Adv. Stud. Contemp. Math. (Kyungshang) 24(2014), no. 1, 5–18. MR 3157404
[3]
D. S. Kim, T. Kim, J.-J. Seo, and S.-H. Lee, Higher-order Changhee numbers and polynomials, Adv. Studies Theor. Phys. 8 (2014), no. 8, 365–373.
[4]
D. S. Kim, T. Kim, Higher-order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 23 (2013), no. 4, 621–636.
[5]
L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, (Translated from the French by J. W. ienhuys), Reidel, Dordrecht, 1974.
[6]
G.-D. Liu and H. M. Srivastava, Explicit formulas for the Nörlund polynomials of the first and second kind, Comput. Math. Appl. 51 (2006), no. 9–10,1377–1384.
[7]
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), no. 3, 288–299. MR 1965383 (2004f:11138).
[8]
T. Kim, Symmetry p-adic invariant integral on Zp for Bernoulli and Euler polynomials, J. Difference Equ. Appl. 14 (2008), no. 12, 1267–1277.MR 2462529 (2009i:11023)
[9]
Z. Zhang and H. Yang, Some closed formulas for generalized Bernoulli-Euler numbers and polynomials, Proc. Jangjeon Math. Soc. 11 (2008), no. 2, 191–198. MR 2482602 (2010a:11036).
[10]
D. Ding and J. Yang, Some identities related to the Apostol -Euler and Apostol Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 20 (2010).no. 1, 7–21. MR 2597988 (2011k:05030).
[11]
K.-W. Hwang, D. V. Dolgy, D. S. Kim, T. Kim, and S. H. Lee, Some theorems on Bernoulli and Euler numbers, Ars Combin. 109 (2013), 285–297.MR 3087218.
[12]
H. M. Srivastava and J.-S. Choi, Series Associated with the Zeta and Related Functions, Kluwer Acad. Publ., Dordrecht, oston and London,2001.
[13]
G. -D. Liu,Generating functions and generalized Euler numbers, Proc. Japan Acad., 84, Ser. A (2008),29-34.
[14]
D.S. Kim, T. Kim, Identities of some special mixed-type polynomials, arXiv:1406.2124v1 [math.NT] 9 Jun 2014.
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