Kyungpook Mathematical Journal

  • 제53권4호
  • /
  • Pages.553-563
  • /
  • 2013
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Identities Involving Euler Polynomials Arising from a Non-linear Differential Equation

  • Rim, Seog-Hoon (Department of Mathematics Education, Kyungpook National University) ;
  • Jeong, Joohee (Department of Mathematics Education, Kyungpook National University) ;
  • Park, Jin-Woo (Department of Mathematics Education, Kyungpook National University)
  • 투고 : 2012.11.15
  • 심사 : 2013.04.09
  • 발행 : 2013.12.23
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초록

We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

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참고문헌

  1. I. N. Cangul and Y. Simsek, A note on interpolation functions of the Frobenius-Euler numbers, in: Application of Mathematics in Technical and Natural Sciences, in AIP Conf. Proc. 1301, Amer. Inst. Phys., Melville, NY(2010), 59-67.
  2. L. Carlitz, Eulerian numbers and polynomials, Math. Mag. 23(1959), 247-260.
  3. L. Carlitz, Note on the integral of the product of several Bernoulli polynomials, J. London Math. Soc. 34(1959), 361-363.
  4. L. Carlitz, The product of two Eulerian polynomials, Math. Mag. 36(1963), 37-41. https://doi.org/10.2307/2688134
  5. K. W. Hwang and D. V. Dolgy and T. Kim and S.S. Lee, On the higher-order q-Euler numbers and polynomials with weight, Discrete Dyn. Nat. Soc. 2011 Article ID 354329, 12page(2011).
  6. L. C. Jang, A study on the distribution of twisted q-Genocchi polynomials, Adv. Stud. Contemp. Math. 18(2)(2009), 181-189.
  7. T. Kim, q-generalized Euler numbers and polynomials, Russian J. Math. Phys. 13(3)(2006), 293-298. https://doi.org/10.1134/S1061920806030058
  8. T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Zp, Russian J. Math. Phys. 16(4)(2009), 484-491. https://doi.org/10.1134/S1061920809040037
  9. T. Kim, New approach to q-Euler polynomials of higher order, Russian J. Math. Phys. 17(2)(2010), 218-225. https://doi.org/10.1134/S1061920810020068
  10. T. Kim, Identities involving Frobenius-Euler polynomials arising from non-linear differential equations, J. of Number Theory, 132(2012), 2854-2865. https://doi.org/10.1016/j.jnt.2012.05.033
  11. N. Nielson, Traite elementaire des nombres de Bernoulli, Paris(1923).
  12. H. Ozden and I.N. Cangul and Y. Simsek, Multivariate interpolation functions of higher-order q-Euler numbers and their applications, Abstract and Applied Analysis 2008 Article ID 390857, 16page(2008).
  13. H. Ozden and I. N. Cangul and Y. Simsek, Remarks on sum of products of (h; q)- twisted Euler polynomials and numbers, J. Inequal. Appl. 2008 Article ID 816129, 8page(2008).
  14. C. S. Ryoo, Some identities of the twisted q-Euler numbers and polynomials associated with q-Bernstein polynomials, Proc. Jangjeon Math. Soc. 14(2011), 239-348.
  15. Y. Simsek, Special functions related to Dedekind-type DC-sums and their applications, Russian J. Math. Phys. 17(4)(2010), 495-508. https://doi.org/10.1134/S1061920810040114
  16. Y. Simsek, Complete sum of products of (h; q)-extension of Euler polynomials and numbers, J. Difference Equ. Appl. 16(11)(2010), 1331-1348. https://doi.org/10.1080/10236190902813967
  17. Y. Simsek and O. Yureki and V. Kurt, On interpolation functions of the twisted generalized Frobenbius-Euler numbers, Adv. Stud. Contemp. Math. 15(2)(2007), 187-194. https://doi.org/10.1016/S1570-579X(07)80026-7

피인용 문헌

  1. Some identities of degenerate Daehee numbers arising from nonlinear differential equation vol.2017, pp.1, 2017, https://doi.org/10.1186/s13662-017-1265-4
  2. Differential equations associated with Catalan–Daehee numbers and their applications vol.111, pp.4, 2017, https://doi.org/10.1007/s13398-016-0349-4