### 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 |
---|---|

Pages (from-to) | 719-730 |

Number of pages | 12 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Publication status | Published - 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

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

**A generalization of mehta-wang determinant and askey-wilson polynomials.** / Guo, Victor J W; Ishikawa, Masao; Tagawa, Hiroyuki; Zeng, Jiang.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - A generalization of mehta-wang determinant and askey-wilson polynomials

AU - Guo, Victor J W

AU - Ishikawa, Masao

AU - Tagawa, Hiroyuki

AU - Zeng, Jiang

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - The askey-wilson polynomials

KW - The mehta-wang determinants

KW - The moments of the little q-jacobi polynomials

UR - http://www.scopus.com/inward/record.url?scp=84887446036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887446036&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84887446036

SP - 719

EP - 730

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1365-8050

ER -