The q-Lah numbers and the nth q-derivative of expq(1/n)

Jacob Katriel
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 45—47
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Authors and affiliations

Jacob Katriel
Department of Chemistry, Technion – Israel Institute of Technology
Haifa 32000, Israel

Abstract

A recently reported nice and surprising property of the Lah numbers is shown to hold for q-Lah numbers as well, i.e., they can be obtained by taking successive q-derivatives of expq(1/n), where expq(x) is the q-exponential.

Keywords

  • q-Lah numbers
  • q-exponential

AMS Classification

  • 11B65
  • 11B73

References

  1. Daboul, S., Mangaldan, J., Spivey, M. Z. & Taylor, P. J. (2013) The Lah numbers and the n‘th derivative of e 1/x
  2. Garsia, A. M. & Remmel, J. (1980) A combinatorial interpretation of q-derangement and q-Laguerre numbers, Europ. J. Combinatorics, 1, 47–59.
  3. Lindsay, J., Mansour, T. & Shattuck, M. (2011) A new combinatorial interpretation of a q-analogue of the Lah numbers, J. Combinatorics, 2, 245–264.
  4. Wagner, C. G. (1996) Generalized Stirling and Lah numbers, Discrete Math., 160, 199–218.

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Cite this paper

APA

Katriel, J. (2017). The q-Lah numbers and the nth q-derivative of expq(1/n). Notes on Number Theory and Discrete Mathematics, 23(2), 45-47.

Chicago

Katriel, Jacob. “The q-Lah Numbers and the nth q-derivative of expq(1/n).” Notes on Number Theory and Discrete Mathematics 23, no. 2 (2017): 45-47.

MLA

Katriel, Jacob. “The q-Lah Numbers and the nth q-derivative of expq(1/n).” Notes on Number Theory and Discrete Mathematics 23.2 (2017): 45-47. Print.

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