Results 1 to 10 of about 901,840 (78)

Moments of Askey-Wilson polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
New formulas for the $n^{\mathrm{th}}$ moment $\mu_n(a,b,c,d;q)$ of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and ...
Jang Soo Kim, Dennis Stanton
doaj   +3 more sources

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
doaj   +2 more sources

Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
Gasper followed the fractional calculus proof of an Erdélyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulation‐based proof of the Erdélyi integral, due to “Joshi and Vyas”. Motivated from this alternative way of
Yashoverdhan Vyas, Anand V. Bhatnagar, Kalpana Fatawat, D. L. Suthar, S. D. Purohit, Serkan Araci   +5 more
wiley   +1 more source

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
wiley   +1 more source

Application of Polynomial Chaos Expansion to Optimize Injection‐Production Parameters under Uncertainty

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, ZhiPing Li, Hong Li, Caspar Daniel Adenutsi, FengPeng Lai, KongJie Wang, Sen Yang, Fazal M. Mahomed   +7 more
wiley   +1 more source

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, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng   +3 more
doaj   +1 more source

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

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
doaj   +1 more source

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
doaj   +1 more source

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, Milton Kist, Marcelo Borges dos Santos, A. Bairi, T. Y. Kam, W. L. Li   +5 more
wiley   +1 more source

Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme

Advances in Mathematical Physics, Volume 2009, Issue 1, 2009., 2009
In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three‐term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of ...
M. Bruschi, F. Calogero, R. Droghei, M. Lakshmanan   +3 more
wiley   +1 more source