PL EN


Preferences help
enabled [disable] Abstract
Number of results
2018 | 101 | 217-221
Article title

Stirling numbers with negative indices

Content
Title variants
Languages of publication
EN
Abstracts
EN
We realize applications of expressions for Stirling numbers with negative indices, in particular, we show that the formulas of Zhi-Hong Sun are consequences of the known identities of Schläfli and Gould.
Publisher

Year
Volume
101
Pages
217-221
Physical description
Contributors
  • Centro de Investigación en Computación, Instituto Politécnico Nacional, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista 07738, CDMX, México
References
  • [1] D. E. Knuth, Selected papers on Discrete Mathematics, CSLI Lecture Notes, No. 106 (2003).
  • [2] J. Quaintance, H. W. Gould, Combinatorial identities for Stirling numbers, World Scientific, Singapore (2016).
  • [3] L. Schläfli, Sur les coefficients du développement du produit 1(1+x)(1+2x)…(1+(n-1)x) suivant les puissance ascendantes de x, Crelle’s Journal 43 (1852) 1-22.
  • [4] J. López-Bonilla, R. López-Vázquez, Harmonic numbers in terms of Stirling numbers of the second kind, Prespacetime Journal 8(2) (2017) 233-234.
  • [5] A. Iturri-Hinojosa, J. López-Bonilla, R. López-Vázquez, O. Salas-Torres, Bernoulli and Stirling numbers, BAOJ Physics 2(1) (2017) 3-5.
  • [6] H. W. Gould, Stirling number representation problems, Proc. Amer. Math. Soc. 11(3) (1960) 447-451.
  • [7] Z-H. Sun, Some inversion formulas and formulas for Stirling numbers, Graphs and Combinatorics 29(4) (2013) 1087-1100
  • [8] J. Riordan, Combinatorial identities, John Wiley & Sons, New York (1968).
  • [9] C. Kramp, Élémens d’arithmétique universelle, Cologne (1808).
  • [10] L. Comtet, Advanced combinatorics. The art of finite and infinite expansions, D. Reidel Pub., Dordrecht, Holland (1974).
  • [11] H. M. Srivastava, J. Choi, Zeta and q-zeta functions and associated series and integrals, Elsevier, London (2012).
  • [12] T. Arakawa, T. Ibukiyama, M. Kaneko, Bernoulli numbers and zeta functions, Springer, Japan (2014).
  • [13] R. Sánchez-Peregrino, The Lucas congruence for Stirling numbers of the second kind, Acta Arithmetica XCIV.1 (2000) 41-52.
  • [14] H. Gupta, Symmetric functions in the theory of integrals numbers, Lucknow University Studies 14, Allahabad Press (1940).
  • [15] H. Gupta, Selected topics in number theory, Tunbridge Wells, Abacus Press, England (1980).
  • [16] I. Gessel, R. P. Stanley, Stirling polynomials, J. of Combinatorial Theory A24 (1978) 24-33.
Document Type
short_communication
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-9398abd5-21f8-4894-9a80-5c1c14f963aa
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.