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Deformed Heisenberg algebra with reflection and d-orthogonal polynomials

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Abstract

This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of d-orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when d = 1. The underlying algebraic framework allowed a systematic derivation of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy.

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Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, King Saud University, P.O.Box 2455, Riyadh, 11451, Saudi Arabia

    Fethi Bouzeffour

  2. Department of mathematics, Faculty of Sciences of Bizerte, Carthage University, P.O.Box 64, Jarzouna, Bizerte, 7021, Tunisia

    Hanen Ben Mansour & Ali Zaghouani

  3. Faculty of Sciences of Tunis, University of Tunis El Manar, B.P. 248 2092, Tunis, Tunisia

    Hanen Ben Mansour & Ali Zaghouani

Authors
  1. Fethi Bouzeffour
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  2. Hanen Ben Mansour
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  3. Ali Zaghouani
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Corresponding author

Correspondence to Fethi Bouzeffour.

Additional information

The first author would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saudi University for funding this Research group No. (RG-1437-020).

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Bouzeffour, F., Ben Mansour, H. & Zaghouani, A. Deformed Heisenberg algebra with reflection and d-orthogonal polynomials. Czech Math J 67, 57–71 (2017). https://doi.org/10.21136/CMJ.2017.0358-15

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  • DOI: https://doi.org/10.21136/CMJ.2017.0358-15

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