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CERTAIN FORMULAS INVOLVING EULERIAN NUMBERS

  • Received : 2013.04.22
  • Accepted : 2013.05.31
  • Published : 2013.09.25

Abstract

In contrast with numerous identities involving the binomial coefficients and the Stirling numbers of the first and second kinds, a few identities involving the Eulerian numbers have been known. The objective of this note is to present certain interesting and (presumably) new identities involving the Eulerian numbers by mainly making use of Worpitzky's identity.

Keywords

References

  1. J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18 (2003), 781-789. https://doi.org/10.4134/CKMS.2003.18.4.781
  2. L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions (Translated from the French by J. W. Nienhuys), Reidel, Dordrecht and Boston, 1974.
  3. J. H. Conway and R. K. Guy, The Book of Numbers, Springer-Verlag, 1996.
  4. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, second edi., Addison-Wesley Publishing Company, 1994.
  5. J. Karamata, Theoremes sur la sommabilite exponentielle et d'autres sommabilit es rattachant, Mathematica (Cluj) 9 (1935), 164-178.
  6. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
  7. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London, and New York, 2012.
  8. J. Worpitzky, Studien uber die Beroullischen and Eulerschen Zahlen, J. Reine Angew. Math. 94 (1883), 203-232.