Results 41 to 50 of about 7,854 (155)
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 +5 more
wiley +1 more source
An eigenvalue problem for the associated Askey-Wilson polynomials [PDF]
, 2012 AmS-LaTeX; 15 ...
Andrea Bruder +2 more
openalex +5 more sources
Multi-indexed Wilson and Askey–Wilson polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2013 As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue ...
Satoru Odake, Ryu Sasaki
openalex +4 more sources
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
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
wiley +1 more source
Asymmetric simple exclusion process with open boundaries and Askey–Wilson polynomials [PDF]
, 2003 We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries.
M. Uchiyama, T. Sasamoto, M. Wadati
semanticscholar +1 more source
Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials [PDF]
, 2009 Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which ...
Alberto Grünbaum +35 more
core +2 more sources
A Polynomial Blossom for the Askey–Wilson Operator [PDF]
Constructive Approximation, 2018 In this paper the authors introduce a blossoming procedure for polynomials related to the Askey-Wilson operator. This blossom is symmetric, multiaffine, and reduces to the complex representation of the polynomial on a certain diagonal. This Askey-Wilson blossom can be used to find the Askey-Wilson derivative of a polynomial of any order.
Simeonov, Plamen, Goldman, Ron
openaire +3 more sources
Casoratian identities for the Wilson and Askey–Wilson polynomials [PDF]
Journal of Approximation Theory, 2015 31 pages, 2 figures. Comments and references added.
Odake, Satoru, Sasaki, Ryu
openaire +2 more sources
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