q-zAl-Salam--Chihara polynomials
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1: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
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31.5.2
►is a polynomial of degree , and hence a solution of (31.2.1) that is analytic at all three finite singularities .
These solutions are the Heun polynomials.
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2: 35.4 Partitions and Zonal Polynomials
§35.4 Partitions and Zonal Polynomials
… ►Normalization
… ►Orthogonal Invariance
… ►Summation
… ►Mean-Value
…3: 24.1 Special Notation
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Bernoulli Numbers and Polynomials
►The origin of the notation , , is not clear. … ►Euler Numbers and Polynomials
… ►The notations , , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …4: 18.3 Definitions
§18.3 Definitions
►Table 18.3.1 provides the definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and normalization (§§18.2(i) and 18.2(iii)). … ►For exact values of the coefficients of the Jacobi polynomials , the ultraspherical polynomials , the Chebyshev polynomials and , the Legendre polynomials , the Laguerre polynomials , and the Hermite polynomials , see Abramowitz and Stegun (1964, pp. 793–801). … ►For another version of the discrete orthogonality property of the polynomials see (3.11.9). … ►Legendre polynomials are special cases of Legendre functions, Ferrers functions, and associated Legendre functions (§14.7(i)). …5: 18 Orthogonal Polynomials
Chapter 18 Orthogonal Polynomials
…6: 18.30 Associated OP’s
§18.30 Associated OP’s
… ► ►Associated Jacobi Polynomials
… ►Associated Legendre Polynomials
… ►For further results on associated Legendre polynomials see Chihara (1978, Chapter VI, §12); on associated Jacobi polynomials, see Wimp (1987) and Ismail and Masson (1991). …7: 18.28 Askey–Wilson Class
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§18.28(iii) Al-Salam–Chihara Polynomials
… ►§18.28(iv) -Al-Salam–Chihara Polynomials
… ►For further nondegenerate cases see Chihara and Ismail (1993) and Christiansen and Ismail (2006). ►§18.28(v) Continuous -Ultraspherical Polynomials
… ►These polynomials are also called Rogers polynomials. …8: 18.1 Notation
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►Nor do we consider the shifted Jacobi polynomials:
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Classical OP’s
… ►Hahn Class OP’s
… ►Wilson Class OP’s
… ►Al-Salam–Chihara: .
9: 18.38 Mathematical Applications
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