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International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 424189, 7 pages
http://dx.doi.org/10.1155/2012/424189
Research Article

Symmetry Fermionic 𝑝 -Adic π‘ž -Integral on β„€ 𝑝 for Eulerian Polynomials

1National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of Korea
2Division of Cultural Education, Kyungnam University, Changwon 631-701, Republic of Korea

Received 18 June 2012; Accepted 14 August 2012

Academic Editor: Cheon Ryoo

Copyright © 2012 Daeyeoul Kim and Min-Soo Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. S. Kim, T. Kim, W. J. Kim, and D. V. Dolgy, β€œA note on Eulerian polynomials,” Abstract and Applied Analysis, vol. 2012, Article ID 269640, 10 pages, 2012. View at Publisher Β· View at Google Scholar
  2. P. Luschny, β€œEulerian polynomials,” http://www.luschny.de/math/euler/EulerianPolynomials.html, 2011.
  3. D. S. Kim and K. H. Park, β€œIdentities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under S3,” Journal of Inequalities and Applications, vol. 2010, Article ID 851521, 16 pages, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. T. Kim, β€œSymmetry p-adic invariant integral on p for Bernoulli and Euler polynomials,” Journal of Difference Equations and Applications, vol. 14, no. 12, pp. 1267–1277, 2008. View at Publisher Β· View at Google Scholar
  5. C. S. Ryoo, β€œA note on q-Bernoulli numbers and polynomials,” Applied Mathematics Letters, vol. 20, no. 5, pp. 524–531, 2007. View at Publisher Β· View at Google Scholar
  6. Y. Simsek, β€œComplete sum of products of (h,q)-extension of Euler polynomials and numbers,” Journal of Difference Equations and Applications, vol. 16, no. 11, pp. 1331–1348, 2010. View at Publisher Β· View at Google Scholar
  7. S. Ramanujan, Collected Papers of Srinivasa Ramanujan, AMS Chelsea Publishing, Providence, RI, USA, 2000.