Gauss–Laguerre formula
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1: 3.5 Quadrature
Gauss–Laguerre Formula
… ► ►${x}_{k}$  ${w}_{k}$  

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${x}_{k}$  ${w}_{k}$  

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2: 6.18 Methods of Computation
3: 18.5 Explicit Representations
§18.5(ii) Rodrigues Formulas
… ►Related formula: … ►Laguerre
… ►For corresponding formulas for Chebyshev, Legendre, and the Hermite ${\mathit{He}}_{n}$ polynomials apply (18.7.3)–(18.7.6), (18.7.9), and (18.7.11). … ►Laguerre
…4: Bibliography G
5: 10.74 Methods of Computation
6: Bibliography M
7: Bibliography T
8: Errata

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In Paragraph Inversion Formula in §35.2, the wording was changed to make the integration variable more apparent.

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In many cases, the links from mathematical symbols to their definitions were corrected or improved. These links were also enhanced with ‘tooltip’ feedback, where supported by the user’s browser.

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The overloaded operator $\equiv $ is now more clearly separated (and linked) to two distinct cases: equivalence by definition (in §§1.4(ii), 1.4(v), 2.7(i), 2.10(iv), 3.1(i), 3.1(iv), 4.18, 9.18(ii), 9.18(vi), 9.18(vi), 18.2(iv), 20.2(iii), 20.7(vi), 23.20(ii), 25.10(i), 26.15, 31.17(i)); and modular equivalence (in §§24.10(i), 24.10(ii), 24.10(iii), 24.10(iv), 24.15(iii), 24.19(ii), 26.14(i), 26.21, 27.2(i), 27.8, 27.9, 27.11, 27.12, 27.14(v), 27.14(vi), 27.15, 27.16, 27.19).
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In Chapter 35 Functions of Matrix Argument, the generalized hypergeometric function of matrix argument ${}_{p}F_{q}({a}_{1},\mathrm{\dots},{a}_{p};{b}_{1},\mathrm{\dots},{b}_{q};\mathbf{T})$, was labeled inadvertently as its single variable counterpart ${}_{p}F_{q}({a}_{1},\mathrm{\dots},{a}_{p};{b}_{1},\mathrm{\dots},{b}_{q};\mathbf{T})$. Furthermore, the Jacobi function of matrix argument ${P}_{\nu}^{(\gamma ,\delta )}\left(\mathbf{T}\right)$, and the Laguerre function of matrix argument ${L}_{\nu}^{(\gamma )}\left(\mathbf{T}\right)$, were also labeled inadvertently (and incorrectly) in terms of the single variable counterparts given by ${P}_{\nu}^{(\gamma ,\delta )}\left(\mathbf{T}\right)$, and ${L}_{\nu}^{(\gamma )}\left(\mathbf{T}\right)$. In order to resolve these inconsistencies, these functions now link correctly to their respective definitions.

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To be consistent with the notation used in (8.12.16), Equation (8.12.5) was changed to read
8.12.5 $$\frac{{\mathrm{e}}^{\pm \pi \mathrm{i}a}}{2\mathrm{i}\mathrm{sin}(\pi a)}Q(a,z{\mathrm{e}}^{\pm \pi \mathrm{i}})=\pm \frac{1}{2}\mathrm{erfc}\left(\pm \mathrm{i}\eta \sqrt{a/2}\right)\mathrm{i}T(a,\eta )$$ 
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Following a suggestion from James McTavish on 20170406, the recurrence relation ${u}_{k}=\frac{(6k5)(6k3)(6k1)}{(2k1)216k}{u}_{k1}$ was added to Equation (9.7.2).

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In §15.2(ii), the unnumbered equation
$$\underset{c\to n}{lim}\frac{F(a,b;c;z)}{\mathrm{\Gamma}\left(c\right)}=\mathbf{F}(a,b;n;z)=\frac{{\left(a\right)}_{n+1}{\left(b\right)}_{n+1}}{(n+1)!}{z}^{n+1}F(a+n+1,b+n+1;n+2;z),$$ $n=0,1,2,\mathrm{\dots}$was added in the second paragraph. An equation number will be assigned in an expanded numbering scheme that is under current development. Additionally, the discussion following (15.2.6) was expanded.
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A bibliographic citation was added in §11.13(i).
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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.