### Abstract

Motivated by the Gaussian symplectic ensemble, Mehta andWang evaluated the n×n determinant det((a+ j -i)Γ(b+j +i)) in 2000. When a = 0, Ciucu and Krattenthaler computed the associated Pfaffian Pf((j -i)Γ(b+ j + i)) with an application to the two dimensional dimer system in 2011. Recently we have generalized the latter Pfaffian formula with a q-analogue by replacing the Gamma function by the moment sequence of the little q-Jacobi polynomials. On the other hand, Nishizawa has found a q-analogue of the Mehta-Wang formula. Our purpose is to generalize both the Mehta-Wang and Nishizawa formulae by using the moment sequence of the little q-Jacobi polynomials. It turns out that the corresponding determinant can be evaluated explicitly in terms of the Askey-Wilson polynomials.

Original language | English |
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Pages (from-to) | 719-730 |

Number of pages | 12 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Publication status | Published - Nov 18 2013 |

Externally published | Yes |

Event | 25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France Duration: Jun 24 2013 → Jun 28 2013 |

### Keywords

- The askey-wilson polynomials
- The mehta-wang determinants
- The moments of the little q-jacobi polynomials

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Discrete Mathematics and Combinatorics

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## Cite this

*Discrete Mathematics and Theoretical Computer Science*, 719-730.