Some discrete multiple orthogonal polynomials [PDF]
, 2003 27 pages, no figures.-- MSC2000 codes: 33C45, 33C10, 42C05, 41A28.-- Issue title: "Proceedings of the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications" (OPSFA-VI, Rome, Italy, 18-22 June 2001).MR#: MR1985676
Arvesú, Jorge +2 more
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Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices [PDF]
, 2005 We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number.
A. F. Nikiforov +15 more
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Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials [PDF]
, 1998 Starting from the second-order difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials ∗pn∗, we find the analytical expressions of the expansion coefficients of any polynomial rm(x) and of the product rm(x)qj(x) in ...
Sánchez Dehesa, Jesús +2 more
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, 2006 For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations.
A. Okounkov +16 more
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Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
, 2011 The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in the ...
Bareiss E H +26 more
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Semi-classical Laguerre polynomials and a third order discrete integrable equation
, 2009 A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is
Christoffel E B +12 more
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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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Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials
, 2020 The discrete orthogonality relations hold for all the orthogonal polynomials obeying three term recurrence relations. We show that they also hold for multi-indexed Laguerre and Jacobi polynomials, which are new orthogonal polynomials obtained by ...
Ho, Choon-Lin, Sasaki, Ryu
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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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Darboux transforms on Band Matrices, Weights and associated Polynomials
, 1999 Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In "Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems", Comm. Math. Phys. 207, pp.
Adler, Mark, van Moerbeke, Pierre
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