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A generalization of Mehta-Wang determinant and Askey-Wilson polynomials
Abstract : Motivated by the Gaussian symplectic ensemble, Mehta and Wang 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 $\mathrm{Pf}((j-i)Γ (b+j+i))$ 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.
Cited literature [13 references]
https://hal.inria.fr/hal-01229667
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:36 AM
Last modification on : Wednesday, July 8, 2020 - 12:43:15 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:33:58 AM
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:36 AM
Last modification on : Wednesday, July 8, 2020 - 12:43:15 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:33:58 AM
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