Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2013, Article ID 629132, 9 pages
Research Article

General Eulerian Numbers and Eulerian Polynomials

1Department of Mathematics and Statistics, Radford University, Radford, VA 24141, USA
2Department of Decision Sciences, San Francisco State University, CA 94132, USA
3Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Received 26 October 2012; Accepted 3 January 2013

Academic Editor: Mike Tsionas

Copyright © 2013 Tingyao Xiong 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.

Linked References

  1. J. Bernoulli, Ars conjectandi, opus posthumum. Accedit tractatus de seriebus infinitis, et epistola gallicè scripta de ludo pilae reticularis, Impensis Thurnisiorum, fratrum, Basel, Switzerland, 1713.
  2. L. Euler, Institutiones calculi differentialis cum eius usu in analysi finitorum ac Doctrina serierumm, chapter VII, Academiae Imperialis Scientiarum Petropolitanae, Petersburg, Russia, 1755.
  3. D. Foata, “Eulerian polynomials: from Euler's time to the present,” in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pp. 253–273, Springer, New York, NY, USA, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  4. L. Euler, “Methodus universalis series summandi ulterius promota,” in Commentarii academia scientiarum imperialis Petropolitana 8, pp. 147–158, Academiae scientiarum imperialis Petropolitanae, 1736. View at Google Scholar
  5. L. Carlitz, “q-Bernoulli and Eulerian numbers,” Transactions of the American Mathematical Society, vol. 76, pp. 332–350, 1954. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Carlitz, “A combinatorial property of q-Eulerian numbers,” The American Mathematical Monthly, vol. 82, pp. 51–54, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Worpitzky, “Studien uber die Bernoullischen und Eulerischen Zahlen,” Journal für die reine und angewandte Mathematik, vol. 94, pp. 203–232, 1883. View at Google Scholar
  8. H. Tsao, “Sums of powers and Eulerian numbers,” The Mathematical Gazette, vol. 95, pp. 347–349, 2011. View at Google Scholar