Advanced Studies in Contemporary Mathematics

Jangjeon Mathematical Society (장전수학회)
권호 표지

A NOTE ON EULERIAN POLYNOMIALS ASSOCIATED WITH BERNOULLI AND EULER NUMBERS AND POLYNOMIALS

  • Kim, D.S. (Department of Mathematics, Sogang University) ;
  • Kim, T. (Department of Mathematics, Kwangwoon University) ;
  • Kim, Y.H. (Division of General Education-Mathematics, Kwangwoon University) ;
  • Dolgy, D.V. (Hanrimwon, Kwangwoon University)
  • Published : 2012.07.01
⟨ Previous Next ⟩

Abstract

The purpose of the present paper is to give some interesting identities of Euerian polynomials in connection with Euler and Bernoulli numbers and polynomials.

Keywords

References

  1. S. Araci, D. Erdal, J. J. Seo, A study on the fermionic p-adic q-integral representation on ${\mathbb{Z}}_p$ associated with weighted q-Bernstein and q-Genocchi polynomials, Abstr. Appl. Anal. 2011 (2011), Art. ID 649248, 10pp.
  2. A. A. Aljinovic, J. Pecaric, Generalizations of weighted Euler identity and Ostrowski type inequalities, Adv. Stud. Contemp. Math. 14 (2007), no. 1, 141-151.
  3. A. Bayad, T. Kim, Identities involving values of Bernstein, q-Bernoulli and q-Euler polynomials, Russ. J. Math. Phys. 18 (2011), 133-143. https://doi.org/10.1134/S1061920811020014
  4. M. Can, M. Cenkci, V. Kurt, Y. Simsek, Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functions, Adv. Stud. Contemp. Math. 18 (2009), no. 2, 135-160.
  5. L. Carlitz, V. E. Jr. Hoggatt, Generalized Eulerian numbers and polynomials, Fibonacci Quart. 16 (1978), no. 2, 138-146.
  6. D. Ding, J. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math. 20 (2010), no. 1, 7-21.
  7. L. Euler, Institutiones calculi differentialis cum eius usu in analysi finitorum ac Doctrina serierum, Academiae Imperialis ScientiarumPetropolitanae, St Petersbourg, 1755, chap. VII(" Methodus summanandi superior ulterius promota").
  8. D. Foata, Eulerian polynomials: from Euler's time to the present, The legacy of Alladi Ramakrishnan in the mathematical sciences, 253-273, Springer, New York, 2010.
  9. D. S. Kim, T. Kim, S.-H. Lee, D. V. Dolgy, S.-H. Rim, Some new identities on the Bernoulli and Euler numbers, Discrete Dyn. Nat. Soc. 2011, Art. ID 856132, 11pp.
  10. D. S. Kim, D. V. Dolgy, T. Kim, S.-H. Rim, Some Formulae for the Product of Two Bernoulli and Euler Polynomials, Abstr. Appl. Anal. 2012 (2012), Article ID 784307, 15pp.
  11. T. Kim, An identity of the symmetry for the Frobenius-Euler polynomials associated with the Fermionic p-adic invariant q-integrals on Zp, Rocky Mountain J. Math. 41 (2011), no. 1, 239-247. https://doi.org/10.1216/RMJ-2011-41-1-239
  12. T. Kim, Some identities on the q-Euler polynomials of higher order and q- Stirling numbers by the fermionic p-adic integral on ${\mathbb{Z}}_p$, Russ. J. Math. Phys. 16 (2009), 484-491. https://doi.org/10.1134/S1061920809040037
  13. T. Kim, On Euler-Barnes multiple zeta functions, Russ. J. Math. Phys. 10 (2003), no. 3, 261-267.
  14. T. Kim, q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients, Russ. J. Math. Phys. 15 (2008), 51-57. https://doi.org/10.1134/S1061920808010068
  15. T. Kim, Symmetry of power sum polynomial and multivariate fermionic p-adic invariant integral on ${\mathbb{Z}}_p$, Russ. J. Math. Phys. 16 (2009), no. 1, 93-96. https://doi.org/10.1134/S1061920809010063
  16. Q.-M. Luo, q-analogues of some results for the Apostol-Euler polynomials, Adv. Stud. Contemp. Math. 20 (2010), no. 1, 103-113.
  17. C. S. Ryoo, Some relations between twisted q-Euler numbers and Bernstein polynomials, Adv. Stud. Contemp. Math. 21 (2011), no. 2, 217-223.
  18. J. P. O. Santos, On a new combinatorial interpretation for a theorem of Euler, Adv. Stud. Contemp. Math. 3 (2001), no. 2, 31-38.
  19. Y. Simsek, O. Yurekli, V. Kurt, On interpolation functions of the twisted generalized Frobenius-Euler numbers, Adv. Stud. Contemp. Math. 15 (2007), no. 2, 187-194,