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Analytic Number Theory, Approximation Theory, and Special Functions pp 239–244Cite as

A Note on q-Stirling Numbers

Abstract

The q-Stirling numbers of both kinds are specializations of the complete or elementary symmetric functions. In this note, we use this fact to prove that the q-Stirling numbers can be expressed in terms of the q-binomial coefficients and vice versa.

Keywords

  • Elementary Symmetric Functions
  • Classical Binomial Coefficients
  • Classical Stirling Numbers
  • Schur Functions
  • Integer Partitions

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References

  1. Andrews, G.E.: The Theory of Partitions. Addison-Wesley Publishing, Reading (1976)

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  2. Call, G.S., Velleman, D.J.: Pascal’s matrices. Amer. Math. Monthly 100(4), 372–376 (1993)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Ernst, T.: q-Stirling numbers, an umbral approach. Adv. Dyn. Syst. Appl. 3(2), 251–282 (2008)

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  4. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Clarendon, Oxford (1995)

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Acknowledgements

The author expresses his gratitude to Oana Merca for the careful reading of the manuscript and helpful remarks.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, A. I. Cuza 13, Craiova, 200585, Romania

    Mircea Merca

Authors
  1. Mircea Merca
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Correspondence to Mircea Merca .

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Editors and Affiliations

  1. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

Additional information

Dedicated to Professor Hari M. Srivastava

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Merca, M. (2014). A Note on q-Stirling Numbers. In: Milovanović, G., Rassias, M. (eds) Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0258-3_9

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