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• W2050713020 abstract "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, Alternative q-Charlier) of any degree and for any order in terms of Pi(x ; q) themselves are proved. We will also provide two other interesting formulae to expand the coefficients of general-order q-difference derivatives Dqpf(x), and for the moments xℓDqpf(x), of an arbitrary function f(x) in terms of its original expansion coefficients. We used the underlying formulae to relate the coefficients of two different polynomial systems of basic hypergeometric orthogonal polynomials, belonging to the Askey–Wilson polynomials and Pn(x ; q) ∈ T. These formulae are useful in setting up the algebraic systems in the unknown coefficients, when applying the spectral methods for solving q-difference equations of any order." @default.
• W2050713020 created "2016-06-24" @default.
• W2050713020 creator A5016529266 @default.
• W2050713020 creator A5076547266 @default.
• W2050713020 date "2010-07-01" @default.
• W2050713020 modified "2023-10-14" @default.
• W2050713020 title "Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials" @default.
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• W2050713020 doi "https://doi.org/10.1016/j.jare.2010.07.001" @default.
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