Recurrence relations for connection coefficients between<b><i>Q</i></b>-orthogonal polynomials of discrete variables in the non-uniform lattice

Álvarez-Nodarse, R.; Ronveaux, A.

doi:10.1088/0305-4470/29/22/016

Cited by 17 publications

(2 citation statements)

References 12 publications

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“…A nonrecursive way to approach this problem, for the case of y = 0, can be found in Álvarez-Nodarse et al [6] and Gasper [36]. Moreover, other authors have considered the problem from a recursive point of view [37,38]. As the connection coefficients a i (n; 0) depend on two parameters i and n, the most interesting recurrence relations are those which leave one of the parameters fixed.…”

Section: Recurrence Relations For Connection Coefficients Between Hahmentioning

confidence: 99%

Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials

Doha

Ahmed²

2006

Integral Transforms and Special Functions

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A formula expressing explicitly the difference derivatives of Hahn polynomials of any degree and for any order in terms of Hahn polynomials themselves is proved. Another explicit formula, which expresses the Hahn expansion coefficients of a general-order difference derivative of an arbitrary polynomial of a discrete variable in terms of its original Hahn coefficients, is also given. A formula for the Hahn coefficients of the moments of one single Hahn polynomial of certain degree is proved. A formula for the Hahn coefficients of the moments of a general-order difference derivative of an arbitrary polynomial of a discrete variable in terms of its Hahn coefficients is also obtained. Application of these formulae for solving ordinary difference equations with varying polynomial coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Hahn-Hahn, Meixner-Hahn, Kravchuk-Hahn and Charlier-Hahn is also developed.

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Section: Recurrence Relations For Connection Coefficients Between Hahmentioning

confidence: 99%

Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials

Doha

Ahmed²

2006

Integral Transforms and Special Functions

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“…Ronveaux et al 47,48] for classical and semiclassical orthogonal polynomials and Lewanowicz 30,34] for classical orthogonal polynomials have proposed alternative, simpler techniques of the same type although they require the knowledge of not only the recurrence relation but also the di erential-di erence relation or/and the second-order di erence equation, respectively, satis ed by the polynomials of the orthogonal set of the expansion problem in consideration. See also 5,11,23,31,45,46] for further description and applications of this method in the discrete case, and 19,32] in the continuous case as well as 3,33] for the q-discrete orthogonality. Koepf and Schmersau 25] has proposed a computer-algebra-based method which, starting from the second order di erence hypergeometric equation, produces by symbolic means and in a recurrent way the expansion coe cients of the classical discrete orthogonal hypergeometric polynomials (CDOHP) in terms of the falling factorial polynomials (already obtained analytically by Lesky 28]; see also 41], 42]) as well as the expansion coe cients of its corresponding inverse problem.…”

mentioning

confidence: 99%

Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials

Álvarez-Nodarse

Yáñez

Dehesa

1998

Journal of Computational and Applied Mathematics

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Starting from the second-order di erence hypergeometric equation satis ed by the set of discrete orthogonal polynomials fp n g, we nd the analytical expressions of the expansion coe cients of any polynomial r m (x) and of the product r m (x)q j (x) in series of the set fp n g. These coe cients are given in terms of the polynomial coe cients of the second-order di erence equations satis ed by the involved discrete hypergeometric polynomials. Here q j (x) denotes an arbitrary discrete hypergeometric polynomial of degree j. The particular cases in which fr m g corresponds to the nonorthogonal families fx m g, the rising factorials or Pochhammer polynomials f(x) m g and the falling factorial or Stirling polynomials fx m] g are considered in detail. The connection problem between discrete hypergeometric polynomials, which here corresponds to the product case with m = 0, is also studied and its complete solution for all the classical discrete orthogonal hypergeometric (CDOH) polynomials is given. Also, the inversion problems of CDOH polynomials associated to the three aforementioned non-orthogonal families are solved.

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On the Connection and Linearization Problem for Discrete Hypergeometric q-Polynomials

Álvarez-Nodarse

Arvesú

Yáñez

2001

Journal of Mathematical Analysis and Applications

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Recurrence relations for connection coefficients betweenQ-orthogonal polynomials of discrete variables in the non-uniform lattice

Cited by 17 publications

References 12 publications

Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials

Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials

Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials

On the Connection and Linearization Problem for Discrete Hypergeometric q-Polynomials

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