§18.41 Tables

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§18.41(i) Polynomials
§18.41(ii) Zeros
§18.41(iii) Other Tables

§18.41(i) Polynomials

Keywords:: Chebyshev polynomials, Hermite polynomials, Laguerre polynomials, Legendre polynomials, classical orthogonal polynomials
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For $\mathop{P_{{n}}\/}\nolimits\!\left(x\right)$ ( $=\mathop{\mathsf{P}_{{n}}\/}\nolimits\!\left(x\right)$ ) see §14.33.

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

§18.41(ii) Zeros

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For $\mathop{P_{{n}}\/}\nolimits\!\left(x\right)$ , $\mathop{L_{{n}}\/}\nolimits\!\left(x\right)$ , and $\mathop{H_{{n}}\/}\nolimits\!\left(x\right)$ 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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For tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).

§18.41 Tables

Contents

§18.41(i) Polynomials

§18.41(ii) Zeros

§18.41(iii) Other Tables