Christoffel coefficients (or numbers)
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1: 3.5 Quadrature
2: Errata

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There have been extensive changes in the notation used for the integral transforms defined in §1.14. These changes are applied throughout the DLMF. The following table summarizes the changes.
Transform New Abbreviated Old Notation Notation Notation Fourier $\mathcal{F}\left(f\right)\left(x\right)$ $\mathcal{F}f\left(x\right)$ Fourier Cosine ${\mathcal{F}}_{c}\left(f\right)\left(x\right)$ ${\mathcal{F}}_{c}f\left(x\right)$ Fourier Sine ${\mathcal{F}}_{s}\left(f\right)\left(x\right)$ ${\mathcal{F}}_{s}f\left(x\right)$ Laplace $\mathcal{L}\left(f\right)\left(s\right)$ $\mathcal{L}f\left(s\right)$ $\mathcal{L}(f(t);s)$ Mellin $\mathcal{M}\left(f\right)\left(s\right)$ $\mathcal{M}f\left(s\right)$ $\mathcal{M}(f;s)$ Hilbert $\mathscr{H}\left(f\right)\left(s\right)$ $\mathscr{H}f\left(s\right)$ $\mathscr{H}(f;s)$ Stieltjes $\mathcal{S}\left(f\right)\left(s\right)$ $\mathcal{S}f\left(s\right)$ $\mathcal{S}(f;s)$ Previously, for the Fourier, Fourier cosine and Fourier sine transforms, either temporary local notations were used or the Fourier integrals were written out explicitly.

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Several changes have been made in §1.16(vii) to

(i)
make consistent use of the Fourier transform notations $\mathcal{F}\left(f\right)$, $\mathcal{F}\left(\varphi \right)$ and $\mathcal{F}\left(u\right)$ where $f$ is a function of one real variable, $\varphi $ is a test function of $n$ variables associated with tempered distributions, and $u$ is a tempered distribution (see (1.14.1), (1.16.29) and (1.16.35));

(ii)
introduce the partial differential operator $\mathbf{D}$ in (1.16.30);

(iii)
clarify the definition (1.16.32) of the partial differential operator $P(\mathbf{D})$; and
 (iv)

(i)

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An entire new Subsection 1.16(viii) Fourier Transforms of Special Distributions, was contributed by Roderick Wong.

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The validity constraint $$ was added to (9.5.6). Additionally, specific source citations are now given in the metadata for all equations in Chapter 9 Airy and Related Functions.

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The relation between ClebschGordan and $\mathit{3}j$ symbols was clarified, and the sign of ${m}_{3}$ was changed for readability. The reference Condon and Shortley (1935) for the ClebschGordan coefficients was replaced by Edmonds (1974) and Rotenberg et al. (1959) and the references for $\mathit{3}j$, $\mathit{6}j$, $\mathit{9}j$ symbols were made more precise in §34.1.

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The website’s icons and graphical decorations were upgraded to use SVG, and additional icons and mousecursors were employed to improve usability of the interactive figures.
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It was reported by Nico Temme on 20150228 that the asymptotic formula for $\mathrm{Ln}\mathrm{\Gamma}\left(z+h\right)$ given in (5.11.8) is valid for $h$ $(\in \u2102)$; originally it was unnecessarily restricted to $[0,1]$.

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In §13.8(iii), a new paragraph with several new equations and a new reference has been added at the end to provide asymptotic expansions for Kummer functions $U(a,b,z)$ and $\mathbf{M}(a,b,z)$ as $a\to \mathrm{\infty}$ in $\mathrm{ph}a\le \pi \delta $ and $b$ and $z$ fixed.

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Because of the use of the $O$ order symbol on the righthand side, the asymptotic expansion (18.15.22) for the generalized Laguerre polynomial ${L}_{n}^{(\alpha )}\left(\nu x\right)$ was rewritten as an equality.

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The entire Section 27.20 was replaced.

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Bibliographic citations have been added or modified in §§2.4(v), 2.4(vi), 2.9(iii), 5.11(i), 5.11(ii), 5.17, 9.9(i), 10.22(v), 10.37, 11.6(iii), 11.9(iii), 12.9(i), 13.8(ii), 13.11, 14.15(i), 14.15(iii), 15.12(iii), 15.14, 16.11(ii), 16.13, 18.15(vi), 20.7(viii), 24.11, 24.16(i), 26.8(vii), 33.12(i), and 33.12(ii).
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A new Subsection 13.29(v) Continued Fractions, has been added to cover computation of confluent hypergeometric functions by continued fractions.
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Subsection 14.18(iii) has been altered to identify Equations (14.18.6) and (14.18.7) as Christoffel’s Formulas.

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A new Subsection 15.19(v) Continued Fractions, has been added to cover computation of the Gauss hypergeometric functions by continued fractions.

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Special cases of normalization of Jacobi polynomials for which the general formula is undefined have been stated explicitly in Table 18.3.1.
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Crossreferences have been added in §§1.2(i), 10.19(iii), 10.23(ii), 17.2(iii), 18.15(iii), 19.2(iv), 19.16(i).
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Entries for the Sage computational system have been updated in the Software Index.

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The default document format for DLMF is now HTML5 which includes MathML providing better accessibility and display of mathematics.

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All interactive 3D graphics on the DLMF website have been recast using WebGL and X3DOM, improving portability and performance; WebGL it is now the default format.
Originally this coefficient was given incorrectly as ${B}_{3}(0)=\frac{\mathrm{430\hspace{0.33em}99056\hspace{0.33em}39368\hspace{0.33em}59253}}{\mathrm{5\hspace{0.33em}68167\hspace{0.33em}34399\hspace{0.33em}42500\hspace{0.33em}00000}}{2}^{\frac{1}{3}}$. The other coefficients in this equation have not been changed.
Reported 20120511 by Antony Lee.
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 $\frac{2(n+\lambda )}{n+1}$.
${p}_{n}(x)$  ${A}_{n}$  ${B}_{n}$  ${C}_{n}$ 

${C}_{n}^{(\lambda )}\left(x\right)$  $\frac{2(n+\lambda )}{n+1}$  $0$  $\frac{n+2\lambda 1}{n+1}$ 
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Reported 20100916 by Kendall Atkinson.