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21: Software Index

… ►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►

This is software of narrow scope developed as a byproduct of a research project and subsequently made available at no cost to the public. The software is often meant to demonstrate new numerical methods or software engineering strategies which were the subject of a research project. When developed, the software typically contains capabilities unavailable elsewhere. While the software may be quite capable, it is typically not professionally packaged and its use may require some expertise. The software is typically provided as source code or via a web-based service, and no support is provided.

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These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

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An increasing number of published books have included digital media containing software described in the book. Often, the collection of software covers a fairly broad area. Such software is typically developed by the book author. While it is not professionally packaged, it often provides a useful tool for readers to experiment with the concepts discussed in the book. The software itself is typically not formally supported by its authors.

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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

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22: DLMF Project News

error generating summary

23: 21.7 Riemann Surfaces

… ►In almost all applications, a Riemann theta function is associated with a compact Riemann surface. …Equation (21.7.1) determines a plane algebraic curve in ${ℂ}^2$, which is made compact by adding its points at infinity. …This compact curve may have singular points, that is, points at which the gradient of $\tilde{P}$ vanishes. … ►In this way, we associate a Riemann theta function with every compact Riemann surface $\mathrm{\Gamma }$. … ►Then the prime form on the corresponding compact Riemann surface $\mathrm{\Gamma }$ is defined by …

24: Preface

… ►Lozier directed the NIST research, technical, and support staff associated with the project, administered grants and contracts, together with Boisvert compiled the Software sections for the Web version of the chapters, conducted editorial and staff meetings, represented the project within NIST and at professional meetings in the United States and abroad, and together with Olver carried out the day-to-day development of the project. … ►Among the research, technical, and support staff at NIST these are B. …

25: About the Project

… ►For acknowledgements of financial support see Funding.

26: 8.27 Approximations

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Luke (1969b, p. 186) gives hypergeometric polynomial representations that converge uniformly on compact subsets of the $z$-plane that exclude $z=0$ and are valid for .

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27: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►For $𝒟(T)$ we can take $C^2(X)$, with appropriate boundary conditions, and with compact support if $X$ is bounded, which space is dense in $L^2\left(X\right)$, and for $X$ unbounded require that possible non-$L^2$ eigenfunctions of (1.18.28), with real eigenvalues, are non-zero but bounded on open intervals, including $\pm \mathrm{\infty }$. …

28: Bibliography I

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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_0(z)-i{J}_1(z)$ and of Bessel functions $J_m(z)$ of any real order $m$ . Linear Algebra Appl. 194, pp. 35–70.

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External Links:

ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt

Referenced by:

§10.21(ix).

Encodings:

BibTeX

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29: 21.9 Integrable Equations

… ►These parameters, including $𝛀$, are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition $u(x,y,0)$ (Deconinck and Segur (1998)). …

30: 24.11 Asymptotic Approximations

… ►uniformly for $x$ on compact subsets of $ℂ$. …