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1: Wadim Zudilin

… ►He has been an Associate Professor at Moscow State University (Russia), an Ostrowski Fellow at Institut Henri Poincaré and Université Paris 6 (France), a Humboldt Fellow at the Cologne University (Germany) and a Visiting Researcher at the Max Planck Institute for Mathematics in Bonn (Germany). …Zudilin is author or coauthor of numerous publications including the book Neverending Fractions, An Introduction to Continued Fractions published by Cambridge University Press in 2014. …Robinson Award of the Canadian Mathematical Society. …

2: Bibliography B

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Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

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External Links:

ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.8(iii).

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An Introduction to Linear Difference Equations. Dover Publications Inc., New York.

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Notes:

Unaltered republication of the original 1927 Harvard University edition.

External Links:

MathReview, ZentralBlatt

Referenced by:

§8.1, Notations P, Notations Q.

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Pi and the AGM, A Study in Analytic Number Theory and Computational Complexity. Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York.

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External Links:

ISBN 0-471-83138-7, MathReview (H. London), ZentralBlatt

Referenced by:

§19.35(i), §19.5, §19.8(i), §23.20(iv).

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Concerning an approximation of Copson. Proc. Amer. Math. Soc. 14 (4), pp. 564–568.

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External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§8.11(v), §8.11(v).

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An analytic continuation of the hypergeometric series. SIAM J. Math. Anal. 18 (3), pp. 884–889.

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External Links:

ISSN 0036-1410, Document, MathReview (H. M. Srivastava), ZentralBlatt

Referenced by:

§15.15, §15.19(i).

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3: Foreword

… ►That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. … ►The document you are now holding, or the Web page you are now reading, represents an effort to extend the legacy of A&S well into the 21st century. … ►This could not have been done without the cooperation of many mathematicians, information technologists, and physical scientists both within NIST and externally. …

4: Viewing DLMF Interactive 3D Graphics

… ►WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a web browser without the use of a plugin. Our WebGL code is based on the X3DOM framework which allows the building of the WebGL application around X3D, an XML based graphics code. …

5: 16.21 Differential Equation

… ►In consequence of (16.19.1) we may assume, without loss of generality, that $p\le q$. With the classification of §16.8(i), when the only singularities of (16.21.1) are a regular singularity at $z=0$ and an irregular singularity at $z=\mathrm{\infty }$. …

6: Guide to Searching the DLMF

… ►From there you can also access an advanced search page where you can control certain settings, narrowing the search to certain chapters, or restricting the results to equations, graphs, tables, or bibliographic items. ►

Table 1: Query Examples

► ►►►

Query	Matching records contain
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int adj sin	$\int$ immediately followed by $\sin$ without any intervening terms.
…

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… ►Wildcards allow matching patterns and marking parts of an expression that don’t matter (as for example, which variable name the author uses for a function): … ►DLMF search is generally case-insensitive except when it is important to be case-sensitive, as when two different special functions have the same standard names but one name has a lower-case initial and the other is has an upper-case initial, such as si and Si, gamma and Gamma. …

7: Bibliography D

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Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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External Links:

Document

Referenced by:

§13.28(iii).

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An Introduction to Chaotic Dynamical Systems. The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA.

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External Links:

ISBN 0-8053-1601-9, MathReview (Richard C. Churchill), ZentralBlatt

Referenced by:

§3.8(viii).

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A program to calculate internal conversion coefficients for all atomic shells without screening. Comput. Phys. Comm. 2 (7), pp. 427–432.

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Notes:

Single-precision Fortran

External Links:

Document, Code

Referenced by:

1st item.

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Solitons: An Introduction. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-33389-X; 0-521-33655-4, MathReview (Peter A. Clarkson), ZentralBlatt

Referenced by:

§22.19(iii), Ch.22.

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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.

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External Links:

ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

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8: DLMF Project News

error generating summary

9: 32.2 Differential Equations

… ►An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however. … ►If $\gamma \delta \ne 0$ in ${\text{P}}_{\text{III}}$, then set $\gamma =1$ and $\delta =-1$, without loss of generality, by rescaling $w$ and $z$ if necessary. If $\gamma =0$ and $\alpha \delta \ne 0$ in ${\text{P}}_{\text{III}}$, then set $\alpha =1$ and $\delta =-1$, without loss of generality. Lastly, if $\delta =0$ and $\beta \gamma \ne 0$, then set $\beta =-1$ and $\gamma =1$, without loss of generality. ►If $\delta \ne 0$ in ${\text{P}}_{\text{V}}$, then set $\delta =-\frac{1}{2}$, without loss of generality. …

10: 8.2 Definitions and Basic Properties

… ►without restrictions on the integration paths. … ►When $z\ne 0$, $\mathrm{\Gamma }(a,z)$ is an entire function of $a$, and $\gamma (a,z)$ is meromorphic with simple poles at $a=-n$, $n=0,1,2,\mathrm{\dots }$, with residue ${(-1)}^n/n!$. … ►without restriction on $a$. …