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On a pair of difference equations for the 4F3 type orthogonal polynomials and related exactly-solvable quantum systems

Elchin Jafarov (UGent) , Nedialka Stoilova (UGent) and Joris Van der Jeugt (UGent)
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Abstract
We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A number of special cases and limit relations are also examined, which allow to introduce similar difference equations for the orthogonal polynomials of the 3F2 and 2F1 types. It is shown that the introduced equations allow to construct new models of exactly-solvable quantum dynamical systems, such as spin chains with a nearest-neighbour interaction and fermionic quantum oscillator models.
Keywords
Racah polynomials, Difference equations

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MLA
Jafarov, Elchin, et al. “On a Pair of Difference Equations for the 4F3 Type Orthogonal Polynomials and Related Exactly-Solvable Quantum Systems.” Springer Proceedings in Mathematics & Statistics, edited by Vladimir Dobrev, vol. 111, Springer, 2014, pp. 291–99, doi:10.1007/978-4-431-55285-7_20.
APA
Jafarov, E., Stoilova, N., & Van der Jeugt, J. (2014). On a pair of difference equations for the 4F3 type orthogonal polynomials and related exactly-solvable quantum systems. In V. Dobrev (Ed.), Springer Proceedings in Mathematics & Statistics (Vol. 111, pp. 291–299). Tokyo, Japan: Springer. https://doi.org/10.1007/978-4-431-55285-7_20
Chicago author-date
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. 2014. “On a Pair of Difference Equations for the 4F3 Type Orthogonal Polynomials and Related Exactly-Solvable Quantum Systems.” In Springer Proceedings in Mathematics & Statistics, edited by Vladimir Dobrev, 111:291–99. Tokyo, Japan: Springer. https://doi.org/10.1007/978-4-431-55285-7_20.
Chicago author-date (all authors)
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. 2014. “On a Pair of Difference Equations for the 4F3 Type Orthogonal Polynomials and Related Exactly-Solvable Quantum Systems.” In Springer Proceedings in Mathematics & Statistics, ed by. Vladimir Dobrev, 111:291–299. Tokyo, Japan: Springer. doi:10.1007/978-4-431-55285-7_20.
Vancouver
1.
Jafarov E, Stoilova N, Van der Jeugt J. On a pair of difference equations for the 4F3 type orthogonal polynomials and related exactly-solvable quantum systems. In: Dobrev V, editor. Springer Proceedings in Mathematics & Statistics. Tokyo, Japan: Springer; 2014. p. 291–9.
IEEE
[1]
E. Jafarov, N. Stoilova, and J. Van der Jeugt, “On a pair of difference equations for the 4F3 type orthogonal polynomials and related exactly-solvable quantum systems,” in Springer Proceedings in Mathematics & Statistics, Varna, Bulgaria, 2014, vol. 111, pp. 291–299.
@inproceedings{7158205,
  abstract     = {{We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. 
A number of special cases and limit relations are also examined, which allow to introduce similar difference equations for the orthogonal polynomials of the 3F2 and 2F1 types. 
It is shown that the introduced equations allow to construct new models of exactly-solvable quantum dynamical systems, such as spin chains with a nearest-neighbour interaction and fermionic quantum oscillator models.}},
  author       = {{Jafarov, Elchin and Stoilova, Nedialka and Van der Jeugt, Joris}},
  booktitle    = {{Springer Proceedings in Mathematics & Statistics}},
  editor       = {{Dobrev, Vladimir}},
  isbn         = {{9784431552840}},
  issn         = {{2194-1009}},
  keywords     = {{Racah polynomials,Difference equations}},
  language     = {{eng}},
  location     = {{Varna, Bulgaria}},
  pages        = {{291--299}},
  publisher    = {{Springer}},
  title        = {{On a pair of difference equations for the 4F3 type orthogonal polynomials and related exactly-solvable quantum systems}},
  url          = {{http://dx.doi.org/10.1007/978-4-431-55285-7_20}},
  volume       = {{111}},
  year         = {{2014}},
}

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