Results 51 to 60 of about 3,345,023 (270)
A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 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
Victor J. W. Guo +3 more
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Bispectrality of Multivariable Racah–Wilson Polynomials [PDF]
Constructive Approximation, 2009 minor ...
Plamen Iliev, Jeffrey S. Geronimo
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Symmetry, 2020 The authors wish to make the following corrections to their paper [...]
H. Cohl, R. S. Costas-Santos, Linus Ge
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The colored Jones polynomials as vortex partition functions
Journal of High Energy Physics, 2021 We construct 3D N $$ \mathcal{N} $$ = 2 abelian gauge theories on S $$ \mathbbm{S} $$ 2 × S $$ \mathbbm{S} $$ 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored ...
Masahide Manabe +2 more
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A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
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Orthogonal Basic Hypergeometric Laurent Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The Askey-Wilson polynomials are orthogonal polynomials in$x = cos heta$, which are given as a terminating $_4phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iheta}$, which are given as a ...
Mourad E.H. Ismail, Dennis Stanton
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Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials [PDF]
, 2014 We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of ...
A. Hoshino, M. Noumi, J. Shiraishi
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An Eigenvalue Problem for the Associated Askey–Wilson Polynomials [PDF]
, 2020 AmS-LaTeX; 15 ...
Sergei K. Suslov +2 more
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Bispectrality of the Complementary Bannai-Ito Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→−1 limit of the Askey-Wilson ...
Vincent X. Genest +2 more
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Nevanlinna Theory of the Wilson Divided-difference Operator [PDF]
Ann. Acad. Sci. Fenn. Math. 42, 175-209 (2017), 2016 Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference equation in terms of the Wilson divided-difference operator.
arxiv +1 more source