Results 21 to 30 of about 2,393 (108)
On Another Characterization of Askey-Wilson Polynomials
Results in Mathematics, 2022 In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} ϕ(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $ϕ$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson ...
Mbouna, D., Suzuki, A.
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A Linear Map Acts as a Leonard Pair with Each of the Generators of U(sl2)
International Journal of Mathematics and Mathematical Sciences, Volume 2020, Issue 1, 2020., 2020 Let ℱ denote an algebraically closed field with a characteristic not two. Fix an integer d ≥ 3; let x, y, and z be the equitable basis of sl2 over ℱ. Let V denote an irreducible sl2‐module with dimension d + 1; let A ∈ End(V). In this paper, we show that if each of the pairs A, x, A, y, and A, z acts on V as a Leonard pair, then these pairs are of ...
Hasan Alnajjar, Luca Vitagliano
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Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 The optimization of oil field development scheme considering the uncertainty of reservoir model is a challenging and difficult problem in reservoir engineering design. The most common method used in this regard is to generate multiple models based on statistical analysis of uncertain reservoir parameters and requires a large number of simulations to ...
Liang Zhang +7 more
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Askey-Wilson Polynomials and Branching Laws
, 2022 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Back, Allen +3 more
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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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Journal of Advanced Research, 2010 Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn ...
Eid H. Doha, Hany M. Ahmed
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A characterization of Askey-Wilson polynomials
Proceedings of the American Mathematical Society, 2019 We show that the only monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$ that satisfy $$ (x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos ,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $ (x)$ is a polynomial of degree at most $4$ and $\mathcal{D}_{q}$ is the Askey-Wilson operator, are Askey-Wilson polynomials and their ...
Nangho, Maurice Kenfack +1 more
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Exceptional 𝑞-Askey-Wilson polynomials and continued fractions [PDF]
Proceedings of the American Mathematical Society, 1991 Two linearly independent solutions of the three-term recurrence relation for the q q -Askey-Wilson polynomials are obtained for the special cases a b c d = q m , m = 1 , 2 , … abcd = {q^m},
Gupta, Dharma P., Masson, David R.
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Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
Nuclear Physics B, 2019 An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form of ...
Pascal Baseilhac, Rodrigo A. Pimenta
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Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 In this paper, the Galerkin method is used to obtain approximate solutions for Kirchhoff plates stochastic bending problem with uncertainty over plates flexural rigidity coefficient. The uncertainty in the rigidity coefficient is represented by means of parameterized stochastic processes. A theorem of Lax‐Milgram type, about existence and uniqueness of
Cláudio Roberto Ávila da Silva Júnior +5 more
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