PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 34 | 2 | 155-166
Tytuł artykułu

Jordan numbers, Stirling numbers and sums of powers

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomial of variable n into the sums of kth powers of consecutive integers from 1 to n is also studied.
Twórcy
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
autor
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
  • [1] Z.I. Borevich and I.R. Szafarevich, Number Theory (Nauka, Moscov, 1964, in Russian).
  • [2] L. Carlitz, Note on the numbers of Jordan and Ward, Duke Math. J. 38 (1971) 783-790. doi: 10.1215/S0012-7094-71-03894-4.
  • [3] L. Carlitz, Some numbers related to the Stirling numbers of the first and second kind, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 544-576 (1976) 49-55.
  • [4] L. Carlitz, Some remarks on the Stirling numbers, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678-715 (1980) 10-14.
  • [5] K. Dilcher, Bernoulli and Euler Polynomials, 587-600 (in F.W.I. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, NIST Handbook of Mathematical Functions, Cambridge Univ. Press, 2010).
  • [6] R.L. Graham, D.E. Knuth and O. Patashnik, Concrete Mathematics (Addison-Wesley, Reading, 1994).
  • [7] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory (Springer, 1990). doi: 10.1007/978-1-4757-1779-2.
  • [8] C. Jordan, Calculus of Finite Differences (Chelsea, New York, 1960). doi: 10.2307/2333783.
  • [9] D.E. Knuth, Johann Faulhaber and sums of powers, Math. Comp. 203 (1993) 277-294. doi: 10.2307/2152953.
  • [10] N. Nielsen, Traité élémentaire des nombers de Bernoulli (Gauthier - Villars, Paris, 1923).
  • [11] S. Rabsztyn, D. Słota and R. Wituła, Gamma and Beta Functions, Part I (Silesian Technical University Press, Gliwice, 2011, in Polish).
  • [12] J. Riordan, An Introduction to Combinatorial Analysis (John Wiley, 1958). doi: 10.1063/1.3060724.
  • [13] J. Riordan, Combinatorial Identities (Wiley, New York, 1968).
  • [14] N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences (http://oeis.org/).
  • [15] M. Živković, On a representation of Stirling's numbers of first kind, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 498-541 (1975) 217-221.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1225
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.