Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NOTE ON EULERIAN POLYNOMIALS OF HIGHER ORDER

  • Choi, Jongsung (Division of General Education-Mathematics Kwangwoon University)
  • Received : 2012.11.28
  • Accepted : 2013.01.11
  • Published : 2013.02.15
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Abstract

In this paper we derive some identities on Eulerian polynomials of higher order from non-linear ordinary differential equations. We show that the generating functions of Eulerian polynomials are solutions of our non-linear ordinary differential equations.

Keywords

References

  1. L. Carlitz, Eulerian numbers and polynomials, Math. Mag. 23 (1959), 247-260.
  2. L. Carlitz, The product of two Eulerian polynomials, Math. Mag. 36 (1963), 37-41. https://doi.org/10.2307/2688134
  3. J. Choi, D. S. Kim, T. Kim, Y. H. Kim, A note on some identities of Frobenius-Euler numbers and polynomials, Int. J. of Math. and Math. Sci., Article ID 861797 (2012), 9 pages.
  4. J. Choi, T. Kim, Y. H. Kim, A note on the q-analogue of Euler numbers and polynomials, Honam Math. J. 33 (2011), no. 4, 529-534. https://doi.org/10.5831/HMJ.2011.33.4.529
  5. J. Choi, T. Kim, Y. H. Kim, B. Lee, On the (w,q)-Euler numbers and polyno-mials with weight ${\alpha}$, Proc. Jongjeon Math. Soc. 15 (2012), no. 1, 91-100.
  6. 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
  7. T. Kim, J. Choi, A note on the product of Frobenius-Euler polynomials arising from the p-adic integral on $\mathbb{Z}p$, Adv. Studies Contemp. Math. 22 (2012), no. 2, 215-223.

Cited by

  1. Some Identities on the High-Order -Euler Numbers and Polynomials with Weight 0 vol.2013, 2013, https://doi.org/10.1155/2013/459763
  2. A note on high order Bernoulli numbers and polynomials using differential equations vol.249, 2014, https://doi.org/10.1016/j.amc.2014.10.074