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21—30 of 864 matching pages
21: Foreword
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►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.
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►However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information.
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.
…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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22: How to Cite
How to Cite
►When citing DLMF from a formal publication, we suggest a format similar to the following: … ►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. Note the ‘E’, ‘F’ and ‘T’ used to disambiguate equations, figures and tables. …23: About MathML
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►, built-in to the browser) support for MathML is growing, (see Browsers supporting MathML).
However, the MathJax javascript library can also used to render the MathML, albeit more slowly.
By default, DLMF will use Native support when available; You may choose how MathML is processed (Native or MathJax) at Customize DLMF.
►In rare cases, a browser lacks both MathML support and a robust enough javascript implementation capable of running MathJax; you may wish to visit the Customize DLMF page and choose the HTML+images document format.
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►Of course you are encouraged to use a modern, up-to-date browser.
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24: 25 Zeta and Related Functions
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25: 13.5 Continued Fractions
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►This continued fraction converges to the meromorphic function of on the left-hand side everywhere in .
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).
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►This continued fraction converges to the meromorphic function of on the left-hand side throughout the sector .
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26: 13.17 Continued Fractions
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►This continued fraction converges to the meromorphic function of on the left-hand side for all .
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).
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►This continued fraction converges to the meromorphic function of on the left-hand side throughout the sector .
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27: 33.21 Asymptotic Approximations for Large
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►We indicate here how to obtain the limiting forms of , , , and as , with and fixed, in the following cases:
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(a)
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(b)
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(c)
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►For asymptotic expansions of and as with and fixed, see Curtis (1964a, §6).
28: 29.7 Asymptotic Expansions
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►As ,
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29.7.5
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►Müller (1966a, b) found three formal asymptotic expansions for a fundamental system of solutions of (29.2.1) (and (29.11.1)) as , one in terms of Jacobian elliptic functions and two in terms of Hermite polynomials.
In Müller (1966c) it is shown how these expansions lead to asymptotic expansions for the Lamé functions and .
Weinstein and Keller (1985) give asymptotics for solutions of Hill’s equation (§28.29(i)) that are applicable to the Lamé equation.
29: Bibliography S
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Algorithm 721: MTIEU1 and MTIEU2: Two subroutines to compute eigenvalues and solutions to Mathieu’s differential equation for noninteger and integer order.
ACM Trans. Math. Software 19 (3), pp. 391–406.
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An Introduction to Classical Electromagnetic Radiation.
Cambridge University Press, Cambridge-New York.
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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions.
J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.
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A Guide to Distribution Theory and Fourier Transforms.
Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.
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An Introduction to Basic Fourier Series.
Developments in Mathematics, Vol. 9, Kluwer Academic Publishers, Dordrecht.
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30: 18.40 Methods of Computation
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