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►The introduction to the eigenvalues and the functions of general order proceeds as in §§28.2(i), 28.2(ii), and 28.2(iii), except that we now restrict ; equivalently .
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►One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the icon) for links to defining formula.
…Errors in the printed Handbook may already have been corrected in the online version; please consult Errata.
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►When citing DLMF from a formal publication, we suggest a format similar to the following:
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►Citations from other electronic media (the web, email, …), should, of course, use the appropriate means to give the site URL (https://dlmf.nist.gov/), or specific Permalinks.
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►The direct correspondence between the reference numbers in the printed Handbook and the permalinks used online in the DLMF enables readers of either version to cite specific items and their readers to easily look them up again — in either version!
►The following table outlines the correspondence between reference numbers as they appear in the Handbook, and the URL’s that find the same item online.
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D. R. Lide (ed.), A Century of Excellence in Measurement, Standards, and Technology,
CRC Press, 2001. The success of the original handbook, widely referred to as “Abramowitz and Stegun” (“A&S”), derived not only from the fact that it provided critically useful scientific data in a highly accessible format, but also because it served to standardize definitions and notations for special functions.
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►The online version, the NIST Digital
Library of Mathematical Functions (DLMF), presents the same technical information along with extensions and innovative interactive features consistent with the new medium.
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►Particular attention is called to the generous support of the National Science Foundation, which made possible the participation of experts from academia and research institutes worldwide.
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►degrees in mathematics from the University of London in 1945, 1948, and 1961, respectively.
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►Olver joined NIST in 1961 after having been recruited by Milton Abramowitz to be the author of the Chapter “Bessel Functions of Integer Order” in the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, a publication which went on to become the most widely distributed and most highly cited publication in NIST’s history.
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►Most notably, he served as the Editor-in-Chief and Mathematics Editor of the onlineNIST Digital Library of Mathematical Functions and its 966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).
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►As a condition of using the DLMF, you explicitly release NIST from any and all liabilities for any damage of any type that may result from errors or omissions in the DLMF.
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Index of Selected Software Within the DLMF Chapters
Within each of the DLMF chapters themselves we will provide a list of
research software for the functions discussed in that chapter.
The purpose of these listings is to provide references to the research
literature on the engineering of software for special functions.
To qualify for listing, the development of the software must have been the subject
of a research paper published in the peer-reviewed literature. If such software
is available online for free download we will provide a link to the software.
In general, we will not index other software within DLMF chapters unless
the software is unique in some way, such as being the only known software
for computing a particular function.
In association with the DLMF we will provide an index of all software for the
computation of special functions covered by the DLMF. It is our intention that
this will become an exhaustive list of sources of software for special functions.
In each case we will maintain a single link where readers can obtain more information
about the listed software. We welcome requests from software authors
(or distributors) for new items to list.
Note that here we will only include software with capabilities that go beyond the
computation of elementary functions in standard precisions since such software is
nearly universal in scientific computing environments.
A. B. Olde Daalhuis and F. W. J. Olver (1995a)Hyperasymptotic solutions of second-order linear differential equations. I.
Methods Appl. Anal.2 (2), pp. 173–197.
A. B. Olde Daalhuis and F. W. J. Olver (1995b)On the calculation of Stokes multipliers for linear differential equations of the second order.
Methods Appl. Anal.2 (3), pp. 348–367.
Unpublished Mathematical Tables (1944)Mathematics of Computation Unpublished Mathematical Tables Collection.
ⓘ
Notes:
Archives of American Mathematics, Center for American History,
The University of Texas at Austin. Covers 1944–1994. An online
guide is arranged chronologically by date of issuance within
Mathematics of Computation
F. Ursell (1984)Integrals with a large parameter: Legendre functions of large degree and fixed order.
Math. Proc. Cambridge Philos. Soc.95 (2), pp. 367–380.
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►These products resulted from the leadership of the Editors and Associate Editors pictured in Figure 1; the contributions of 29 authors, 10 validators, and 5 principal developers; and assistance from a large group of contributing developers, consultants, assistants and interns.
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►It was fortunate that the project had already recruited Adri Olde Daalhuis from the University of Edinburgh in 2012 to serve as an additional Mathematics Editor.
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►They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information online and in handbooks; and in the presentation of mathematics on the web.
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