# On the Korobov and Changhee mixed-type polynomials and numbers

Volume 17, Issue 3, pp 400-407 Publication Date: July 23, 2017

### Authors

Byung Moon Kim - Department of Mechanical System Engineering, Dongguk University, Gyeongju, 780-714, Korea.
Jeong Gon Lee - Division of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute,Wonkwang University, Iksan 570-749, Republic of Korea.
Lee-Chae Jang - Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea.
Sangki Choi - Department of Mathematics Education, Konkuk University, Seoul 143-701, Korea.

### Abstract

By using the Bosonic p-adic integral, Kim et al. [D. S. Kim, T. Kim, H.-I. Kwon, J.-J. Seo, Adv. Stud. Theor. Phys., 8 (2014), 745–754] studied some identities of the Korobov and Daehee mixed-type polynomials. In this paper, by using the fermionic p-adic integral, we define the Korobov and Changhee mixed-type polynomials and give some interesting identities of those polynomials.

### Keywords

• Korobov polynomials
• Changhee polynomials
• Korobov and Changhee mixed-type polynomials.

### 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, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51–88.

• [3] D. V. Dolgiĭ, D. S. Kim, T. Kim, On Korobov polynomials of the first kind, (Russian) Mat. Sb., 208 (2017), 65–79.

• [4] D. V. Dolgy, D. S. Kim, T. Kim, S.-H. Rim, Some identities of special q-polynomials, J. Inequal. Appl., 2014 (2014 ), 10 pages.

• [5] D. V. Dolgy, T. Kim, H.-I. Kwon, Identities of symmetry for the higher-order Carlitz’s degenerate q-Euler polynomials under the symmetry group of degree 3, Adv. Stud. Contemp. Math. (Kyungshang), 26 (2016), 595–600.

• [6] T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 9 (2002), 288–299.

• [7] T. Kim, Identities involving Laguerre polynomials derived from umbral calculus, Russ. J. Math. Phys., 21 (2014), 36–45.

• [8] T. Kim, D. V. Dolgy, D. S. Kim, S.-H. Rim, A note on the identities of special polynomials, Ars Combin, 113A (2014), 97–106.

• [9] T. Kim, D. V. Dolgy, D. S. Kim, J.-J. Seo, Differential equations for Changhee polynomials and their applications, J. Nonlinear Sci. Appl., 9 (2016), 2857–2864.

• [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 of degenerate special polynomials, Open Math., 13 (2015), 380–389.

• [12] D. S. Kim, T. Kim, Some identities of Korobov-type polynomials associated with p-adic integrals on $Z_p$, Adv. Difference Equ., 2015 (2015 ), 13 pages.

• [13] T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88–92.

• [14] D. S. Kim, T. Kim, D. V. Dolgy, Some properties of special polynomials, Appl. Math. Sci., 8 (2014), 8559–8564.

• [15] D. S. Kim, T. Kim, H.-I. Kwon, T. Mansour, Nonlinear differential equation for Korobov numbers, Adv. Stud. Contemp. Math. (Kyungshang), 26 (2016), 733–740.

• [16] D. S. Kim, T. Kim, H.-I. Kwon, J.-J. Seo, Identities of some special mixed-type polynomials, Adv. Stud. Theor. Phys., 8 (2014), 745–754.

• [17] D. S. Kim, T. Kim, S.-H. Lee, D. V. Dolgy, Some special polynomials and Sheffer sequences, J. Comput. Anal. Appl., 16 (2014), 702–712.

• [18] D. S. Kim, T. Kim, S.-H. Rim, Some identities arising from Sheffer sequences of special polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 681–693.

• [19] T. Kim, D. S. Kim, J.-J. Seo, H.-I. Kwon, Differential equations associated with $\lambda$-Changhee polynomials, J. Nonlinear Sci. Appl., 9 (2016), 3098–3111.

• [20] T. Kim, H.-I. Kwon, J. J. Seo, Degenerate q-Changhee polynomials, J. Nonlinear Sci. Appl., 9 (2016), 2389–2393.

• [21] 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), ChebyshevskiĭSb., 1 (2001), 40–49.