대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권3호
  • /
  • Pages.741-749
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  • 2015
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE n-TH TWISTED CHANGHEE POLYNOMIALS AND NUMBERS

  • Rim, Seog-Hoon (Department of Mathematics Education Kyungpook National University) ;
  • Park, Jin-Woo (Department of Mathematics Education Daegu University) ;
  • Pyo, Sung-Soo (Department of Mathematics Education Kyungpook National University) ;
  • Kwon, Jongkyum (Department of Mathematics Kyungpook National University)
  • 투고 : 2013.11.06
  • 발행 : 2015.05.31
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초록

The Changhee polynomials and numbers are introduced in [6]. Some interesting identities and properties of those polynomials are derived from umbral calculus (see [6]). In this paper, we consider Witt-type formula for the n-th twisted Changhee numbers and polynomials and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials.

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참고문헌

  1. S. Araci and M. Acikgoz, A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials, Adv. Stud. Contemp. Math. 22 (2012), no. 3, 399-406.
  2. A. Bayad, Modular properties of elliptic Bernoulli and Euler functions, Adv. Stud. Contemp. Math. 20 (2010), no. 3, 389-401.
  3. J. Choi, D. S. Kim, T. Kim, and Y. H. Kim, Some arithmetic identities on Bernoulli and Euler numbers arising from the p-adic integrals on $\mathbb{Z}_p$, Adv. Stud. Contemp. Math. 22 (2012), no. 2, 239-247.
  4. D. Ding and J. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math. 20 (2010), no. 1, 7-21.
  5. D. S. Kim, T. Kim, Y. H. Kim, and D. V. Dolgy, A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials, Adv. Stud. Contemp. Math. 22 (2012), no. 3, 379-389.
  6. D. S. Kim, T. Kim, and J. J. Seo, A note on Changhee polynomials and numbers, Adv. Studies Theor. Phys. 7 (2013), no. 20, 993-1003.
  7. T. Kim, Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys. 10 (2003), no. 1, 91-98.
  8. T. Kim, p-adic q-integrals associated with the Changhee-Barnes' q-Bernoulli polynomials, Integral Transforms Spec. Funct. 15 (2004), no. 5, 415-420. https://doi.org/10.1080/10652460410001672960
  9. T. Kim, D. S. Kim, T. Mansour, S.-H. Rim, M. and Schork Umbral calculus and Sheffer sequences of polynomials, J. Math. Phys. 54 (2013), no. 8, 083504, 15 pp.
  10. T. Kim and S.-H. Rim, On Changhee-Barnes' q-Euler numbers and polynomials, Adv. Stud. Contemp. Math. 9 (2004), no. 2, 81-86.
  11. T. Kim and S.-H. Rim, New Changhee q-Euler numbers and polynomials associated with p-adic q-integrals, Comput. Math. Appl. 54 (2007), no. 4, 484-489. https://doi.org/10.1016/j.camwa.2006.12.028
  12. Q.-M. Luo, q-analogues of some results for the Apostol-Euler polynomials, Adv. Stud. Contemp. Math. 20 (2010), no. 1, 103-113.
  13. C. S. Ryoo, T. Kim, and R. P. Agarwal, Exploring the multiple Changhee q-Bernoulli polynomials, Int. J. Comput. Math. 82 (2005), no. 4, 483-493. https://doi.org/10.1080/00207160512331323362
  14. C. S. Ryoo and H. Song, On the real roots of the Changhee-Barnes' q-Bernoulli polyno-mials, Proceedings of the 15th International Conference of the Jangjeon Mathematical Society, 63-85, Jangjeon Math. Soc., Hapcheon, 2004.
  15. Y. Simsek, Special functions related to Dedekind-type DC-sums and their applications, Russ. J. Math. Phys. 17 (2010), no. 4, 495-508. https://doi.org/10.1134/S1061920810040114
  16. Y. Simsek, T. Kim, and I. S. Pyung, Barnes' type multiple Changhee q-zeta functions, Adv. Stud. Contemp. Math. 10 (2005), no. 2, 121-129.

피인용 문헌

  1. Some new and explicit identities related with the Appell-type degenerate q-Changhee polynomials vol.2016, pp.1, 2016, https://doi.org/10.1186/s13662-016-0912-5
  2. Symmetric Properties of Carlitz’s Type q-Changhee Polynomials vol.10, pp.11, 2018, https://doi.org/10.3390/sym10110634
  3. Differential equations associated with degenerate Changhee numbers of the second kind pp.1579-1505, 2018, https://doi.org/10.1007/s13398-018-0576-y
  4. -Changhee Polynomials and Numbers vol.2018, pp.1607-887X, 2018, https://doi.org/10.1155/2018/9520269