Realizations of $su(1,1)$ and $U_q(su(1,1))$ and generating functions for orthogonal polynomials
, 1998 Positive discrete series representations of the Lie algebra $su(1,1)$ and the quantum algebra $U_q(su(1,1))$ are considered. The diagonalization of a self-adjoint operator (the Hamiltonian) in these representations and in tensor products of such ...
Jagannathan, R., Van der Jeugt, J.
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MathematicsIn the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete–continuous Sobolev-type inner product defined in terms of the Jacobi measure.
Roberto S. Costas-Santos
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$q$-Classical orthogonal polynomials: A general difference calculus approach
, 2009 It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator.
A.F. Nikiforov +26 more
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Discrete and Differential Equations in Applied Mathematics
Communications, 2008 In the contribution we map investigations performed in mathematics at the Faculty of Science in 2003-2007. Main directions developed at the faculty are described and some of the latest achievements are presented.
Miroslava Ruzickova
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Multiple Meixner Polynomials on a Non-Uniform Lattice
Mathematics, 2020 We consider two families of type II multiple orthogonal polynomials. Each family has orthogonality conditions with respect to a discrete vector measure.
Jorge Arvesú +1 more
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An efficient computation of discrete orthogonal moments for bio-signals reconstruction
EURASIP Journal on Advances in Signal Processing, 2022 Bio-signals are extensively used in diagnosing many diseases in wearable devices. In signal processing, signal reconstruction is one of the essential applications.
Islam S. Fathi +2 more
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Using $\D$-operators to construct orthogonal polynomials satisfying higher order difference or differential equations [PDF]
, 2013 We introduce the concept of $\D$-operators associated to a sequence of polynomials $(p_n)_n$ and an algebra $\A$ of operators acting in the linear space of polynomials.
Durán, Antonio J.
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Uniform Asymptotics for Discrete Orthogonal Polynomials with Respect to Varying Exponential Weights on a Regular Infinite Lattice [PDF]
, 2009 We consider the large N asymptotics of a system of discrete orthogonal polynomials on an infinite regular lattice of mesh N1/N, with weight e −NV (x) , where V (x) is a real analytic function with sufficient growth at infinity.
P. Bleher, Karl Liechty
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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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Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions
Journal of Mathematics, 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 ...
Yashoverdhan Vyas +4 more
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