Differential equations for Changhee polynomials and their applications
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Authors
Taekyun Kim
- Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea.
Dmitry V. Dolgy
- Institute of Mathematics and Computer Science, Far Eastern Federal University, 690950 Vladivostok, Russia.
Dae San Kim
- Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea.
Jong Jin Seo
- Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea.
Abstract
Recently, the non-linear Changhee differential equations were introduced by Kim and Kim [T. Kim, D.
S. Kim, Russ. J. Math. Phys., 23 (2016), 1-5] and these differential equations turned out to be very useful
for studying special polynomials and mathematical physics. Some interesting identities and properties
of Changhee polynomials can also be derived from umbral calculus (see [D. S. Kim, T. Kim, J. J. Seo,
Adv. Studies Theor. Phys., 7 (2013), 993-1003]). In this paper, we consider differential equations arising
from Changhee polynomials and derive some new and explicit formulae and identities from our differential
equations.
Share and Cite
ISRP Style
Taekyun Kim, Dmitry V. Dolgy, Dae San Kim, Jong Jin Seo, Differential equations for Changhee polynomials and their applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2857--2864
AMA Style
Kim Taekyun, Dolgy Dmitry V., Kim Dae San, Seo Jong Jin, Differential equations for Changhee polynomials and their applications. J. Nonlinear Sci. Appl. (2016); 9(5):2857--2864
Chicago/Turabian Style
Kim, Taekyun, Dolgy, Dmitry V., Kim, Dae San, Seo, Jong Jin. "Differential equations for Changhee polynomials and their applications." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2857--2864
Keywords
- Changhee polynomials
- differential equations.
MSC
References
-
[1]
A. Bayad, J. Chikhi , Apostol-Euler polynomials and asymptotics for negative binomial reciprocals, Adv. Stud. Contemp. Math., 24 (2014), 33-37.
-
[2]
L.-C. Jang, C. S. Ryoo, J. J. Seo, H. I. kwon, Some properties of the twisted Changhee polynomials and their zeros, Appl. Math. Comput., 274 (2016), 169-177.
-
[3]
T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys., 10 (2003), 91-98.
-
[4]
D. S. Kim, T. Kim, A note on Boole polynomials, Integral Transforms Spec. Funct., 25 (2014), 627-633.
-
[5]
D. S. Kim, T. Kim, Some identities of Korobov-type polynomials associated with p-adic integrals on \(\mathbb{Z}_p\), Adv. Difference Equ., 2015 (2015), 13 pages.
-
[6]
T. Kim, D. S. Kim , A note on non-linear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 1-5.
-
[7]
D. S. Kim, T. Kim, T. Komatsu, S.-H. Lee, Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials, Adv. Difference Equ., 2014 (2014), 22 pages.
-
[8]
D. S. Kim, T. Kim, J. J. Seo, A Note on Changhee Polynomials and Numbers, Adv. Studies Theor. Phys., 7 (2013), 993-1003.
-
[9]
T. Kim, T. Mansour , Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys., 21 (2014), 484-493.
-
[10]
D. V. Kruchinin, V. V. Kruchinin , Application of a composition of generating functions for obtaining explicit formulas of polynomials, J. Math. Anal. Appl., 404 (2013), 161-171.
-
[11]
H. I. Kwon, T. Kim, J. J. Seo, A note on degenerate Changhee numbers and polynomials, Proc. Jangjeon Math.Soc., 18 (2015), 295-305.
-
[12]
J. Kwon, H. S. Noh, S. H. Jeong, A. J. Kim, J. H. Lee, S.-H. Rim, A Note on weighted Changhee Polynomials and Numbers, Adv. Studies. Theor. Phys., 9 (2015), 191-198.
-
[13]
J.-W. Park, On the twisted q-Changhee polynomials of higher order, J. Comput. Anal. Appl., 20 (2016), 424-431.
-
[14]
S.-H. Rim, J.-W. Park, S.-S. Pyo, J. Kwon, The n-th twisted Changhee polynomials and numbers, Bull. Korean Math. Soc., 52 (2015), 741-749.
-
[15]
C. S. Ryoo, T. Kim, R. P. Agarwal, Exploring the multiple Changhee q-Bernoulli polynomials, Int. J. Comput. Math., 82 (2005), 483-493.
-
[16]
C. S. Ryoo, H. Song, R. P. Agarwal, On the roots of the q-analogue of Euler-Barnes' polynomials, Adv. Stud. Contemp. Math., 9 (2004), 153-163.
-
[17]
G. Y. Sohn, J. K. Kwon, A note on twisted Changhee polynomials and numbers with weight, Appl. Math. Sci., 9 (2015), 1517-1525.
-
[18]
A. V. Ustinov , Korobov polynomials and umbral analysis, Chebyshevskii Sb., 4 (2003), 137-152.
-
[19]
N. L. Wang, H. Li , Some identities on the Higher-order Daehee and Changhee Numbers, Pure Appl. Math. J., 4 (2015), 33-37.