Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

1Citations
Citations of this article
8Readers
Mendeley users who have this article in their library.

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. © 2010 Cairo University.

Cite

CITATION STYLE

APA

Doha, E. H., & Ahmed, H. M. (2010). Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials. Journal of Advanced Research, 1(3), 193–207. https://doi.org/10.1016/j.jare.2010.07.001

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free