Geodesic
Deformed Heisenberg algebra with reflection and $d$-orthogonal polynomials
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 57-71.

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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.
DOI : 10.21136/CMJ.2017.0358-15
Classification : 22E47, 33C45, 33D15
Keywords: $d$-orthogonal polynomials; matrix element; coherent state; hypergeometric function; Meixner polynomials; $d$-dimensional linear functional vector 
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Bouzeffour, Fethi; Ben Mansour, Hanen; Zaghouani, Ali. Deformed Heisenberg algebra with reflection and $d$-orthogonal polynomials. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 57-71. doi : 10.21136/CMJ.2017.0358-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0358-15/

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