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Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x) Cover

Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x)

Open Access
|Aug 2016

References

  1. [1] J. C. Ahuja, E. A. Enneking, Concavity property and a recurrence relation for associated Lah numbers, Fibonacci Quart., 17 (2) (1979), 158–161.
  2. [2] P. Barry, Some Observations on the Lah and Laguerre Transforms of Integer Sequences, Journal of Integer Sequences, 10 (2007), Article 07.4.6
  3. [3] K. N. Boyadzhiev, Power Series with Binomial Sums and Asymptotic Expansions, Int. Journal of Math. Analysis, 8 (28) (2014), 1389–1414.10.12988/ijma.2014.45126
  4. [4] K. N. Boyadzhiev, Exponential polynomials, Stirling numbers, and evaluation of some Gamma integrals, Abstract and Applied Analysis, Volume 2009, Article ID 168672 (electronic, open source).10.1155/2009/168672
  5. [5] K. N. Boyadzhiev, A Series transformation formula and related polynomials, International Journal of Mathematics and Mathematical Sciences, 2005 (2005), Issue 23, 3849–3866.10.1155/IJMMS.2005.3849
  6. [6] Y. A. Brychkov, Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas, Chapman and Hall/CRC, 2008.10.1201/9781584889571
  7. [7] Charalambos A. Charalambides, Jagbir Singh, A review of the Stirling numbers, their generalizations and statistical interpretations, Comm. Statist. Theory Methods, 17 (8) (1988), 2533–2595.10.1080/03610928808829760
  8. [8] C. A. Charalambides, Enumerative Combinatorics, Chapman and Hall/CRC, 2002.
  9. [9] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Co., Dordrecht, 1974.10.1007/978-94-010-2196-8
  10. [10] S. Daboul, J. Mangaldan, M. Z. Spivey, P. J. Taylor, The Lah Numbers and the nth Derivative of exp(1/x), Math. Magazine, 86 (1) (2013) 39–47.10.4169/math.mag.86.1.039
  11. [11] H. W. Gould, Combinatorial Identities, Published by the author, 1972.
  12. [12] Bai-Ni Guo, F. Qi, Six proofs for an identity of the Lah numbers, Online Journal of Analytic Combinatorics, 10 (2015).
  13. [13] Bai-Ni Guo, F. Qi, Some integral representations and properties of Lah numbers (arxiv.org), 2014.
  14. [14] N. N. Lebedev, Special Functions and Their Applications, Dover, 1972.
  15. [15] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.
  16. [16] M. Petkovšek, T. Pisanski, Combinatorial interpretation of unsigned Stirling and Lah numbers, Preprint 40 (2002), Univ. of Ljubljana. (Available on the internet.)
  17. [17] E. D. Rainville, Special Functions, Chelsea, 1971.
  18. [18] I. J. Schwatt, An Introduction to the Operations with Series, Chelsea, 1924.
  19. [19] P. G. Todorov, Taylor expansions of analytic functions related to (1 + z)x − 1, J. Math. Anal. Appl.,132 (1988), 264–280.10.1016/0022-247X(88)90060-1
Language: English
Page range: 22 - 31
Submitted on: May 4, 2015
Published online: Aug 2, 2016
Published in print: Aug 1, 2016
Published by: Sapientia Hungarian University of Transylvania
In partnership with: Paradigm Publishing Services

© 2016 Khristo N. Boyadzhiev, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.