DOI QR코드

DOI QR Code

NOTE ON STIRLING POLYNOMIALS

  • Received : 2013.05.01
  • Accepted : 2013.07.08
  • Published : 2013.08.15

Abstract

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

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. I. Gessel and R. P. Stanley, Stirling polynomials, J. Comb. Theor. ser. A 24 (1978), 24-33.
  5. J. Ginsburg, Note on Stirling's numbers, Amer. Math. Monthly 35 (1928), 77-80. https://doi.org/10.2307/2299462
  6. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, second edi., Addison-Wesley Publishing Company, 1994.
  7. J. Karamata, Theoremes sur la sommabilite exponentielle et d'autres sommabilites rattachant, Mathematica (Cluj) 9 (1935), 164-178.
  8. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  9. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
  10. 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.
  11. H. M. Srivastava and P. G. Todorov, An explicit formula for the generalized Bernoulli polynomials, J. Math. Anal. Appl. 130 (1988), 509-513. https://doi.org/10.1016/0022-247X(88)90326-5
  12. J. Worpitzky, Studien uber die Beroullischen and Eulerschen Zahlen, J. Reine Angew. Math. 94 (1883), 203-232.