DOI QR코드

DOI QR Code

A RELATION OF GENERALIZED q-ω-EULER NUMBERS AND POLYNOMIALS

  • 투고 : 2017.03.26
  • 심사 : 2017.05.12
  • 발행 : 2017.05.30

초록

In this paper, we study the generalizations of Euler numbers and polynomials by using the q-extension with p-adic integral on $\mathbb{Z}_p$. We call these: the generalized q-${\omega}$-Euler numbers $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and polynomials $E^{({\alpha})}_{n,q,{\omega}}(x;a)$. We investigate some elementary properties and relations for $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and $E^{({\alpha})}_{n,q,{\omega}}(x;a)$.

키워드

참고문헌

  1. N.S. Jung and C.S. Ryoo, A research on a new approach to Euler polynomials and Bernstein polynomials with variable $[x]_q$, J. Appl. Math. & Informatics 35 (2017), 205-215. https://doi.org/10.14317/jami.2017.205
  2. T. Kim, q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys. 14 (2007), 15-27. https://doi.org/10.2991/jnmp.2007.14.1.3
  3. H.Y. Lee and C.S. Ryoo, A note on recurrence formula for values of the Euler zeta functions ${\zeta}_E(2n)$ at positive integers, Bull. Korean Math. Soc. 51 (2014), 1425-1432 https://doi.org/10.4134/BKMS.2014.51.5.1425
  4. H.Y. Lee, N.S. Jung and C.S. Ryoo, Generalized w-Euler numbers and polynomials, ISRN Applied Mathematics 2012 (2012), 475463, 14 pages.
  5. C.S. Ryoo, A numerical investigation on the structure of the roots of q-Genocchi polynomials, J. Appl. Math. Comput. 26 (2008), 325-332. https://doi.org/10.1007/s12190-007-0011-6
  6. C.S. Ryoo, A numerical investigation on the zeros of the tangent polynomials, J. Appl. Math. & Informatics 32 (2014), 315-322. https://doi.org/10.14317/jami.2014.315
  7. C.S. Ryoo, A note on the zeros of the q-Bernoulli polynomials, J. Appl. Math. & Informatics 28 (2010), 805-811.
  8. C.S. Ryoo, Re ection symmetries of the q-Genocchi polynomials, J. Appl. Math. & Informatics 28 (2010), 1277-1284.
  9. C.S. Ryoo, H.Y. Lee and N.S. Jung, Some identities on the (h, q)-Euler numbers with weight and q-Bernstein polynomials, Applied Mathematical Sciences 5 (2011), 3429 - 3437.