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21: 24.4 Basic Properties

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§24.4(i) Difference Equations

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§24.4(ii) Symmetry

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§24.4(vi) Special Values

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§24.4(vii) Derivatives

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22: 18.10 Integral Representations

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Ultraspherical

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Legendre

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Jacobi

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Ultraspherical

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Laguerre

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23: 18.5 Explicit Representations

§18.5 Explicit Representations

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Laguerre

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Hermite

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24: 18.35 Pollaczek Polynomials

§18.35 Pollaczek Polynomials

… ►There are 3 types of Pollaczek polynomials: … ►For the monic polynomials … ► … ► …

25: 24.16 Generalizations

§24.16 Generalizations

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Polynomials and Numbers of Integer Order

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Nörlund Polynomials

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§24.16(ii) Character Analogs

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§24.16(iii) Other Generalizations

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26: 18.18 Sums

§18.18 Sums

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Ultraspherical

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Legendre

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Hermite

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27: 29.20 Methods of Computation

… ►These matrices are the same as those provided in §29.15(i) for the computation of Lamé polynomials with the difference that $n$ has to be chosen sufficiently large. … ►A fourth method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree. … ►

§29.20(ii) Lamé Polynomials

… ►The corresponding eigenvectors yield the coefficients in the finite Fourier series for Lamé polynomials. … ►

§29.20(iii) Zeros

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28: 18.34 Bessel Polynomials

§18.34 Bessel Polynomials

… ►Often only the polynomials (18.34.2) are called Bessel polynomials, while the polynomials (18.34.1) and (18.34.3) are called generalized Bessel polynomials. … … ►

§18.34(ii) Orthogonality

… ►expressed in terms of Romanovski–Bessel polynomials, Laguerre polynomials or Whittaker functions, we have …

29: 18.17 Integrals

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Jacobi

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Laguerre

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Ultraspherical

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Legendre

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Hermite

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30: 35.11 Tables

§35.11 Tables

►Tables of zonal polynomials are given in James (1964) for $|\kappa |\le 6$, Parkhurst and James (1974) for $|\kappa |\le 12$, and Muirhead (1982, p. 238) for $|\kappa |\le 5$. Each table expresses the zonal polynomials as linear combinations of monomial symmetric functions.