orthogonality properties
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1: 12.16 Mathematical Applications
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►Sleeman (1968b) considers certain orthogonality properties of the PCFs and corresponding eigenvalues.
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2: 18.3 Definitions
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Table 18.3.1: Orthogonality properties for classical OP’s: intervals, weight functions, normalizations, leading coefficients, and parameter constraints.
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►In addition to the orthogonal property given by Table 18.3.1, the Chebyshev polynomials , , are orthogonal on the discrete point set comprising the zeros , of :
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►For another version of the discrete orthogonality property of the polynomials see (3.11.9).
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Name | Constraints | ||||||
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3: 18.19 Hahn Class: Definitions
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Table 18.19.1: Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s: discrete sets, weight functions, normalizations, and parameter constraints.
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Hahn, Krawtchouk, Meixner, and Charlier
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4: 18.34 Bessel Polynomials
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§18.34(ii) Orthogonality
…5: 3.11 Approximation Techniques
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►They enjoy an orthogonal property with respect to integrals:
…as well as an orthogonal property with respect to sums, as follows.
When and , ,
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►The in (3.11.11) can be calculated from (3.11.10), but in general it is more efficient to make use of the orthogonal property (3.11.9).
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6: 14.17 Integrals
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§14.17(iii) Orthogonality Properties
…7: 18.5 Explicit Representations
8: 18.35 Pollaczek Polynomials
9: 18.27 -Hahn Class
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►All these systems of OP’s have orthogonality properties of the form
…Some of the systems of OP’s that occur in the classification do not have a unique orthogonality property.
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►They are defined by their -hypergeometric representations, followed by their orthogonality properties.
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