2010
DOI: 10.1016/j.jare.2010.07.001
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Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

Abstract: Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials P n (x ; q) ∈ T (T ={P n (x ; q) ∈ Askey-Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn, Alternative q-Charlier) of any degree and for any order in terms of P i (x ; q) themselves are proved. We will also provide two other interesting formulae to expand the coefficients of general-order q-difference derivatives D p q f (x), and for the moments x D … Show more

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Cited by 3 publications
(4 citation statements)
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“…The theoretical and numerical analysis of numerous physical and mathematical problems very often requires the expansion of an arbitrary polynomial or the expansion of an arbitrary function with its q-derivatives and moments into a set of q-classical orthogonal polynomials. This is also true for the basic hypergeometric orthogonal polynomials belonging to the Askey-Wilson scheme which appear to be important in certain problems of mathematical physics as described for example in [7], [12].…”
Section: Introductionmentioning
confidence: 86%
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“…The theoretical and numerical analysis of numerous physical and mathematical problems very often requires the expansion of an arbitrary polynomial or the expansion of an arbitrary function with its q-derivatives and moments into a set of q-classical orthogonal polynomials. This is also true for the basic hypergeometric orthogonal polynomials belonging to the Askey-Wilson scheme which appear to be important in certain problems of mathematical physics as described for example in [7], [12].…”
Section: Introductionmentioning
confidence: 86%
“…q −n+j , q α+j+1 q α+m+j+1 q; q n+m−j is simplified using the q-analogue of the Vandermonde summation formula [17, Eq. (1.11.4)] [12]). For m ≤ n,…”
Section: Computation Ofmentioning
confidence: 99%
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“…In his recent work [7,5,6] Doha develops a class of spectral-Galerkin methods for the direct solution of higher order differential equations. One of particular interest here is the Jacobi formula, based on finite Jacobi expansion in terms of power of x.…”
Section: Introductionmentioning
confidence: 99%