defined by contour integrals
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1: 9.14 Incomplete Airy Functions
2: 1.10 Functions of a Complex Variable
§1.10(viii) Functions Defined by Contour Integrals
…3: 2.10 Sums and Sequences
4: 21.7 Riemann Surfaces
5: 1.9 Calculus of a Complex Variable
§1.9(iii) Integration
… ►If $x(t)$ and $y(t)$ are continuous and ${x}^{\prime}(t)$ and ${y}^{\prime}(t)$ are piecewise continuous, then $z(t)$ defines a contour. … ►A simple closed contour is a simple contour, except that $z(a)=z(b)$. … ►Winding Number
…6: Errata

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In Equations (15.6.1)–(15.6.9), the Olver hypergeometric function $\mathbf{F}(a,b;c;z)$, previously omitted from the lefthand sides to make the formulas more concise, has been added. In Equations (15.6.1)–(15.6.5), (15.6.7)–(15.6.9), the constraint $$ has been added. In (15.6.6), the constraint $$ has been added. In Section 15.6 Integral Representations, the sentence immediately following (15.6.9), “These representations are valid when $$, except (15.6.6) which holds for $$.”, has been removed.

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In Subsection 25.2(ii) Other Infinite Series, it is now mentioned that (25.2.5), defines the Stieltjes constants ${\gamma}_{n}$. Consequently, ${\gamma}_{n}$ in (25.2.4), (25.6.12) are now identified as the Stieltjes constants.
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Additional keywords are being added to formulas (an ongoing project); these are visible in the associated ‘info boxes’ linked to the icons to the right of each formula, and provide better search capabilities.

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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

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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));

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

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clarify the definition (1.16.32) of the partial differential operator $P(\mathbf{D})$; and
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(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.
The scaling error reported on 20160912 by Dan Piponi also applied to contour and density plots for the phase of the hyperbolic umbilic canonical integrals. Scales were corrected in all figures. The interval $8.4\le \frac{xy}{\sqrt{2}}\le 8.4$ was replaced by $12.0\le \frac{xy}{\sqrt{2}}\le 12.0$ and $12.7\le \frac{x+y}{\sqrt{2}}\le 4.2$ replaced by $18.0\le \frac{x+y}{\sqrt{2}}\le 6.0$. All plots and interactive visualizations were regenerated to improve image quality.
(a) Contour plot.  (b) Density plot. 
Figure 36.3.18: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,0\right)$.
(a) Contour plot.  (b) Density plot. 
Figure 36.3.19: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,1\right)$.
(a) Contour plot.  (b) Density plot. 
Figure 36.3.20: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,2\right)$.
(a) Contour plot.  (b) Density plot. 
Figure 36.3.21: Phase of hyperbolic umbilic canonical integral $\mathrm{ph}{\mathrm{\Psi}}^{(\mathrm{H})}\left(x,y,3\right)$.
Reported 20160928.

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A number of changes were made with regard to fractional integrals and derivatives. In §1.15(vi) a reference to Miller and Ross (1993) was added, the fractional integral operator of order $\alpha $ was more precisely identified as the RiemannLiouville fractional integral operator of order $\alpha $, and a paragraph was added below (1.15.50) to generalize (1.15.47). In §1.15(vii) the sentence defining the fractional derivative was clarified. In §2.6(iii) the identification of the RiemannLiouville fractional integral operator was made consistent with §1.15(vi).

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Changes to §8.18(ii)–§8.11(v): A sentence was added in §8.18(ii) to refer to Nemes and Olde Daalhuis (2016). Originally §8.11(iii) was applicable for real variables $a$ and $x=\lambda a$. It has been extended to allow for complex variables $a$ and $z=\lambda a$ (and we have replaced $x$ with $z$ in the subsection heading and in Equations (8.11.6) and (8.11.7)). Also, we have added two paragraphs after (8.11.9) to replace the original paragraph that appeared there. Furthermore, the interval of validity of (8.11.6) was increased from $$ to the sector $$, and the interval of validity of (8.11.7) was increased from $\lambda >1$ to the sector $\lambda >1$, $\mathrm{ph}a\le \frac{3\pi}{2}\delta $. A paragraph with reference to Nemes (2016) has been added in §8.11(v), and the sector of validity for (8.11.12) was increased from $\mathrm{ph}z\le \pi \delta $ to $\mathrm{ph}z\le 2\pi \delta $. Two new Subsections 13.6(vii), 13.18(vi), both entitled Coulomb Functions, were added to note the relationship of the Kummer and Whittaker functions to various forms of the Coulomb functions. A sentence was added in both §13.10(vi) and §13.23(v) noting that certain generalized orthogonality can be expressed in terms of Kummer functions.

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Four of the terms in (14.15.23) were rewritten for improved clarity.
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In applying changes in Version 1.0.12 to (16.15.3), an editing error was made; it has been corrected.
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Meta.Numerics (website) was added to the Software Index.
Originally the term $\sqrt{1+2\eta}$ was given incorrectly as $\sqrt{1+\eta}$ in this equation and in the line above. Additionally, for improved clarity, the modulus $k=1/\sqrt{2+{\eta}^{1}}$ has been defined in the line above.
Reported 20140502 by Svante Janson.