Weight Function Approach to q-Difference Equations for the q-Hypergeometric Polynomials |
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| Authors: | A. S. Hegazi M. Mansour |
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| Affiliation: | (1) Mathematics Department, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt |
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| Abstract: | In this paper we define a new algebra generated by the difference operators Dq and Dq-1 with two analytic functions  (x) and  (x). Also, we define an operator M = J1J2–J3J4 s.t. all q-hypergeometric orthogonal polynomials Yn(x), x  cos( ), are eigenfunctions of the operator M with eigenvalues  q[n]q. The choice of (x) and (x) depend on the weight function of Yn(x). |
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| Keywords: | weight function q-difference equations q-hypergeometric polynomials |
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