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21: Bibliography R

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Tables of the integrals and differential coefficients of $\mathrm{Gi}(+x)$ and $\mathrm{Hi}(-x)$ . Quart. J. Mech. Appl. Math. 7 (3), pp. 379–384.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

(9.12.30), (9.12.31), §9.12(viii), §9.16, 2nd item.

Encodings:

BibTeX

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22: 29.15 Fourier Series and Chebyshev Series

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§29.15(i) Fourier Coefficients

… ►A convenient way of constructing the coefficients, together with the eigenvalues, is as follows. … ►

29.15.9 $${[A_1,A_3,\mathrm{\dots },A_{2n+1}]}^{\mathrm{T}},$$

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Symbols:

$n$: nonnegative integer and $A_{2p}$: coefficients

Permalink:

http://dlmf.nist.gov/29.15.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §29.15(i), §29.15(i), §29.15 and Ch.29

… ►This determines the polynomial $P$ of degree $n$ for which ${\mathrm{𝑢𝐸}}_{2n}^m(z,k^2)=P({\mathrm{sn}}^2(z,k))$; compare Table 29.12.1. The set of coefficients of this polynomial (without normalization) can also be found directly as an eigenvector of an $(n+1)\times (n+1)$ tridiagonal matrix; see Arscott and Khabaza (1962). …

23: Bibliography K

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Pascal program for generating tables of $\mathrm{SU}(3)$ Clebsch-Gordan coefficients. Comput. Phys. Comm. 85 (1), pp. 82–88.

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External Links:

ISSN 0010-4655, Document, Code, MathReview Entry, ZentralBlatt

Referenced by:

6th item.

Encodings:

BibTeX

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24: Bibliography

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Numerical Tables for Angular Correlation Computations in $\alpha$-, $\beta$- and $\gamma$-Spectroscopy: $3j$-, $6j$-, $9j$-Symbols, F- and $\mathrm{\Gamma }$-Coefficients. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, Springer-Verlag.

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External Links:

ISBN 978-3-540-04218-1

Referenced by:

§34.14.

Encodings:

BibTeX

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25: 10.20 Uniform Asymptotic Expansions for Large Order

… ►Note: Another way of arranging the above formulas for the coefficients $A_k(\zeta ),B_k(\zeta ),C_k(\zeta )$, and $D_k(\zeta )$ would be by analogy with (12.10.42) and (12.10.46). … ►For (10.20.14) and further information on the coefficients see Temme (1997). ►For numerical tables of $\zeta =\zeta (z)$, ${(4\zeta /(1-z^2))}^{\frac{1}{4}}$ and $A_k(\zeta )$, $B_k(\zeta )$, $C_k(\zeta )$, and $D_k(\zeta )$ see Olver (1962, pp. 28–42). … ►For resurgence properties of the coefficients (§2.7(ii)) see Howls and Olde Daalhuis (1999). … …

26: Errata

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The coefficient $A_n$ for $C_n^{(\lambda )}\left(x\right)$ in the first row of this table originally omitted the parentheses and was given as $\frac{2n+\lambda }{n+1}$, instead of $\frac{2(n+\lambda )}{n+1}$.

$p_n(x)$	$A_n$	$B_n$	$C_n$
$C_n^{(\lambda )}\left(x\right)$	$\frac{2(n+\lambda )}{n+1}$	$0$	$\frac{n+2\lambda -1}{n+1}$
⋮

Reported 2010-09-16 by Kendall Atkinson.

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27: 10.41 Asymptotic Expansions for Large Order

… ►For numerical tables of $\eta =\eta (z)$ and the coefficients $U_k(p)$, $V_k(p)$, see Olver (1962, pp. 43–51). …

28: 3.10 Continued Fractions

… ►For several special functions the $S$-fractions are known explicitly, but in any case the coefficients $a_n$ can always be calculated from the power-series coefficients by means of the quotient-difference algorithm; see Table 3.10.1. …

29: 10.21 Zeros

… ►For numerical coefficients for $m=2,3,4,5$ see Olver (1951, Tables 3–6). … ►The latter reference includes numerical tables of the first few coefficients in the uniform asymptotic expansions. …

30: 18.20 Hahn Class: Explicit Representations

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18.20.1 $$p_n(x)=\frac{1}{{\kappa }_n{w}_x}{\nabla }_x^n\left(w_x\prod _{\mathrm{\ell }=0}^{n-1}F(x+\mathrm{\ell })\right),$$ $x\in X$.

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Symbols:

${\nabla }_x$: backward difference, $\in$: element of, $p_n(x)$: polynomial of degree $n$ , $w_x$: weights, $X$: subset of $ℝ$ , $\mathrm{\ell }$: nonnegative integer, $n$: nonnegative integer, $x$: real variable, $F(x)$: coefficient and ${\kappa }_n$: coefficient

A&S Ref:

22.17.2

Referenced by:

§18.20(i), Table 18.20.1

Permalink:

http://dlmf.nist.gov/18.20.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §18.20(i), §18.20(i), §18.20 and Ch.18

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