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Abstract and Applied Analysis
Volume 2008, Article ID 296159, 10 pages
http://dx.doi.org/10.1155/2008/296159
Research Article

On the -Extension of Apostol-Euler Numbers and Polynomials

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, South Korea
2Natural Science Institute, KonKuk University, Chungju 380-701, South Korea
3Department of Mathematics and Computer Science, KonKuk University, Chungju 380-701, South Korea

Received 4 October 2008; Accepted 21 November 2008

Academic Editor: Lance Littlejohn

Copyright © 2008 Young-Hee Kim et al. 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.

Citations to this Article [20 citations]

The following is the list of published articles that have cited the current article.

  • KyoungHo Park, and Young-Hee Kim, “On Some Arithmetical Properties of the Genocchi Numbers and Polynomials,” Advances in Difference Equations, vol. 2008, no. 1, pp. 195049, 2008. View at Publisher · View at Google Scholar
  • Taekyun Kim, Lee-Chae Jang, Young-Hee Kim, and Kyung-Won Hwang, “On the Identities of Symmetry for the Generalized Bernoulli Polynomials Attached to chi of Higher Order,” Journal Of Inequalities And Applications, 2009. View at Publisher · View at Google Scholar
  • Taekyun Kim, Seog-Hoon Rim, and Byungje Lee, “Some identities of symmetry for the generalized bernoulli numbers and polynomials,” Abstract and Applied Analysis, vol. 2009, 2009. View at Publisher · View at Google Scholar
  • Taekyun Kim, and Young-Hee Kim, “On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomia ls,” Journal of Inequalities and Applications, 2009. View at Publisher · View at Google Scholar
  • Kyung-Won Hwang, Young-Hee Kim, and Taekyun Kim, “Sums of products of q -euler polynomials and numbers,” Journal of Inequalities and Applications, vol. 2009, 2009. View at Publisher · View at Google Scholar
  • Kyung-Won Hwang, Young-Hee Kim, and Taekyun Kim, “Interpolation Functions of-Extensions of Apostol's Type Euler Polynomials,” Journal of Inequalities and Applications, 2009. View at Publisher · View at Google Scholar
  • Hacer Ozden, Yilmaz Simsek, and H.M. Srivastava, “A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials,” Computers & Mathematics with Applications, vol. 60, no. 10, pp. 2779–2787, 2010. View at Publisher · View at Google Scholar
  • Taekyun Kim, Lee-Chae Jang, Young-Hee Kim, and Seog-Hoon Rim, “New Approach to q-Euler Numbers and Polynomials,” Advances in Difference Equations, vol. 2010, pp. 1–10, 2010. View at Publisher · View at Google Scholar
  • L.-C. Jang, H. Yi, K. Shivashankara, T. Kim, Y. H. Kim, and B. Lee, “A Note on Symmetric Properties of the Twisted q-Bernoulli Polynomials and the Twisted Generalized q-Bernoulli Polynomials,” Advances in Difference Equations, vol. 2010, pp. 1–14, 2010. View at Publisher · View at Google Scholar
  • Qiu-Ming Luo, and H.M. Srivastava, “Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5702–5728, 2011. View at Publisher · View at Google Scholar
  • Hacer Ozden, “Generating Functions of the Unified Representation of the Bernoulli, Euler and Genocchi Polynomials of Higher Order,” Numerical Analysis and Applied Mathematics Icnaam 2011: International Confe, vol. 1389, 2011. View at Publisher · View at Google Scholar
  • Srivastava, and Junesang Choi2012. View at Publisher · View at Google Scholar
  • Yilmaz Simsek, “Unification of the Bernstein-type polynomials and their applications,” Boundary Value Problems, 2013. View at Publisher · View at Google Scholar
  • Rahime Dere, Yilmaz Simsek, and H.M. Srivastava, “A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra,” Journal of Number Theory, vol. 133, no. 10, pp. 3245–3263, 2013. View at Publisher · View at Google Scholar
  • Hacer Ozden, and Yilmaz Simsek, “Unified representation of the family of L-functions,” Journal of Inequalities and Applications, 2013. View at Publisher · View at Google Scholar
  • Yilmaz Simsek, “Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications,” Fixed Point Theory and Applications, vol. 2013, no. 1, pp. 87, 2013. View at Publisher · View at Google Scholar
  • Hacer Ozden, and Yilmaz Simsek, “Modification and unification of the Apostol-type numbers and polynomials and their applications,” Applied Mathematics and Computation, vol. 235, pp. 338–351, 2014. View at Publisher · View at Google Scholar
  • Qiu-Ming Luo, “Elliptic extensions of the Apostol-Bernoulli and Apostol-Euler polynomials,” Applied Mathematics and Computation, vol. 261, pp. 156–166, 2015. View at Publisher · View at Google Scholar
  • Srivastava, Mohammad Masjed-Jamei, and Mohammad Reza Beyki, “A parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials,” Applied Mathematics and Information Sciences, vol. 12, no. 5, pp. 907–916, 2018. View at Publisher · View at Google Scholar
  • Serkan Araci, Waseem Khan, and Kottakkaran Nisar, “Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ,” Symmetry, vol. 10, no. 12, pp. 675, 2018. View at Publisher · View at Google Scholar