An Eigenvalue Problem for the Associated Askey–Wilson Polynomials
An Eigenvalue Problem for the Associated Askey–Wilson Polynomials
To derive an eigenvalue problem for the associated Askey-Wilson polynomials, we consider an auxiliary function in two variables which is related to the associated Askey-Wilson polynomials introduced by Ismail and Rahman. The Askey-Wilson operator, applied in each variable separately, maps this function to the ordinary Askey-Wilson polynomials with different sets of parameters. A third Askey-Wilson operator is found with the help of a computer algebra program which links the two, and an eigenvalue problem is stated.
AmS-LaTeX; 15 pages
- Arizona State University United States
- University of Vienna Austria
- Colorado College United States
Primary 33D45, 42C10, Secondary 33D15, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 101012 Kombinatorik, 101012 Combinatorics
Primary 33D45, 42C10, Secondary 33D15, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 101012 Kombinatorik, 101012 Combinatorics
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