Titlebook: Hypergeometric Orthogonal Polynomials and Their q-Analogues; Roelof Koekoek,Peter A. Lesky,René F. Swarttouw Book 20101st edition Springer

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Orthogonal Polynomial Solutions in ,(,+,) of Real Difference Equationsnd . with degree[..]=. of polynomials where .∈{1,2,3,…} or .→∞. The polynomials ..(.) and ..(.) are called dual polynomials with respect to the sequences of eigenvalues . and . when ..(..)=..(..) for all .,.=0,1,2,…,..

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Orthogonal Polynomial Solutions in ,(,+,) of Complex Difference Equationsse that the coefficients are complex. In that case we look for polynomial solutions ..(.(.+.)) with .∈ℂ and .∈ℝ. The three-term recurrence relations (7.4.1) and (7.4.2) still hold with . replaced by .. Again we set .=.+. with .∈ℝ and .∈ℝ. Then we have . For .=−2. the imaginary part cancels and we have .(.+.)=−..−... Now we define

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Hypergeometric Orthogonal Polynomials and Their q-Analogues978-3-642-05014-5Series ISSN 1439-7382 Series E-ISSN 2196-9922

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