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

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Book 20101st edition. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all

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Polynomial Solutions of Eigenvalue Problems,∈ℝ∖{−1,0}, .∈ℝ and (.,.)≠(1,0). This class of operators includes the .-derivative operator . (.=0), the difference operator Δ (.=1 and .=1) and also the differentiation operator . as a limit case (.→1 and .=0). In order to avoid the latter limiting process, we introduce the operator . in a second wa

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Hypergeometric Orthogonal Polynomialsgonal polynomials we state the most important properties such as a representation as a hypergeometric function, orthogonality relation(s), the three-term recurrence relation, the second-order differential or difference equation, the forward shift (or degree lowering) and backward shift (or degree ra

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Orthogonal Polynomial Solutions in ,,+,, of Real ,-Difference Equations2)) . with .∈{1,2,3,…} or .→∞, where . with . where .,.,.,..,..∈ℝ, .>0, .≠1 and .≠0. If the regularity condition (11.2.4) holds all eigenvalues . are different. This implies by using theorem 3.7 that there exists a sequence of dual polynomials. In this case we have . with .=0 and ..=1=... Furthermor

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