18 Orthogonal Polynomials Computation 18.40 Methods of Computation 18.42 Software

§18.41 Tables

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Referenced by:: Erratum (V1.1.6) for Chapters 10 Bessel Functions, 18 Orthogonal Polynomials, 34 3j, 6j, 9j Symbols
Permalink:: http://dlmf.nist.gov/18.41
See also:: Annotations for Ch.18

§18.41(i) Polynomials

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Keywords:: Chebyshev polynomials, Hermite polynomials, Laguerre polynomials, Legendre polynomials, classical orthogonal polynomials, tables
Permalink:: http://dlmf.nist.gov/18.41.i
See also:: Annotations for §18.41 and Ch.18

For $P_{n}\left(x\right)$ ( $=\mathsf{P}_{n}\left(x\right)$ ) see §14.33.

Abramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates $T_{n}\left(x\right)$ , $U_{n}\left(x\right)$ , $L_{n}\left(x\right)$ , and $H_{n}\left(x\right)$ for $n=0(1)12$ . The ranges of $x$ are $0.2(.2)1$ for $T_{n}\left(x\right)$ and $U_{n}\left(x\right)$ , and $0.5,1,3,5,10$ for $L_{n}\left(x\right)$ and $H_{n}\left(x\right)$ . The precision is 10D, except for $H_{n}\left(x\right)$ which is 6-11S.

§18.41(ii) Zeros

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Permalink:: http://dlmf.nist.gov/18.41.ii
See also:: Annotations for §18.41 and Ch.18

For $P_{n}\left(x\right)$ , $L_{n}\left(x\right)$ , and $H_{n}\left(x\right)$ see §3.5(v). See also Abramowitz and Stegun (1964, Tables 25.4, 25.9, and 25.10).

§18.41(iii) Other Tables

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Permalink:: http://dlmf.nist.gov/18.41.iii
See also:: Annotations for §18.41 and Ch.18

For tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).

18.40 Methods of Computation 18.42 Software

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§18.41 Tables

Contents

§18.41(i) Polynomials

§18.41(ii) Zeros

§18.41(iii) Other Tables

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