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A RECURRENCE FORMULA FOR q-EULER NUMBERS OF HIGHER ORDER

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In this paper, we consider Carlitz's type q-Euler numbers and polynomials of higher order and give a recurrence formula for these q-Euler numbers and polynomials of higher order. We obtain a distribution relation for the q-Euler polynomials and have some identities for the q-Euler numbers and polynomials.

Abstract

In this paper, we consider Carlitz's type q-Euler numbers and polynomials of higher order and give a recurrence formula for these q-Euler numbers and polynomials of higher order. We obtain a distribution relation for the q-Euler polynomials and have some identities for the q-Euler numbers and polynomials.

참고문헌 (14)

  1. L. Carlitz, "q-Bernoulli numbers and polynomials", Duke Mathematical Journal, 15, pp.987~1000 (1948)
  2. L. Carlitz, "q-Bernoulli Eulerian numbers", Transactions of the American Mathematical Society, 75, pp.332~350 (1954)
  3. T. Kim, "q-Euler numbers and polynomials associated with p-adic q-integrals", Journal of Non-linear Mathematical Physics, 14, pp.15~27 (2007)
  4. T. Kim, "On the q-extension of Euler and Genocchi numbers", Journal of Mathematical Analysis and Applications, 326, pp.1458~1465 (2007)
  5. Taekyun Kim, "The modified q-Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 16(2), pp.161~170 (2008), 장전수학회
  6. T. Kim, "Note on the Euler q-zeta functions", J. of Number Theory, 129, pp.1798~1804 (2009)
  7. T. Kim, "Some identities on the q-Euler polynomials of higher order and q-Sirling numbers by the fermionic p-adic integral on Zp", Russian Journal of Mathematical Physics, 16, pp.484~491 (2009)
  8. T. Kim, "New approach to q-Euler numbers and polynomials", Advances in Difference Equations, 2010, pp.9~ (2010)
  9. Y.-H. Kim, "On the q-extension of Apostol-Euler numbers and polynomials", Abstract and Applied Analysis, 2008, pp.10~ (2008)
  10. T. Kim, "Barnes-type multiple q-Zeta functions and q-Euler polynomials", J. Phys. A: Math. Theor, 43, pp.255201~ (2010)
  11. 김태균, "NOTE ON CARLITZ’S TYPE q-EULER NUMBERS AND POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 13(2), pp.149~155 (2010), 장전수학회
  12. H. Ozden, "Remarks on q-Bernoulli numbers associated with Daehee numbers", Advanced Studies in Contemporary Mathematics, 18(1), pp.41~48 (2009), 장전수학회
  13. H. Ozden, "A new extension of q-Euler numbers and polynomials related to their interpolation functions", Applied Mathematics Letters, 21, pp.934~939 (2008)
  14. H. Ozden, "A note on p -adic q -Euler measure", Advanced Studies in Contemporary Mathematics, 14(2), pp.233~240 (2007), 장전수학회

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