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21: 36.14 Other Physical Applications

… ►Applications include scattering of elementary particles, atoms and molecules from particles and surfaces, and chemical reactions. …

22: 7.24 Approximations

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§7.24(i) Approximations in Terms of Elementary Functions

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23: Bibliography U

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Elementary Number Theory. McGraw-Hill Book Company, Inc., New York.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.10(iii).

Encodings:

BibTeX

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24: 19.15 Advantages of Symmetry

… ►Symmetry allows the expansion (19.19.7) in a series of elementary symmetric functions that gives high precision with relatively few terms and provides the most efficient method of computing the incomplete integral of the third kind (§19.36(i)). …

25: 30.4 Functions of the First Kind

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§30.4(ii) Elementary Properties

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26: Notices

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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.

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27: 6.20 Approximations

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§6.20(i) Approximations in Terms of Elementary Functions

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28: 18.24 Hahn Class: Asymptotic Approximations

… ►In particular, asymptotic formulas in terms of elementary functions are given when $z=x$ is real and fixed. … ►Dunster (2001b) provides various asymptotic expansions for $C_n(x;a)$ as $n\to \mathrm{\infty }$, in terms of elementary functions or in terms of Bessel functions. …

29: 1.11 Zeros of Polynomials

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§1.11(ii) Elementary Properties

… ►The elementary symmetric functions of the zeros are (with $a_n\ne 0$) …

30: 10.16 Relations to Other Functions

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Elementary Functions

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$$H_{\frac{1}{2}}^{(2)}\left(z\right)=\mathrm{i}{H}_{-\frac{1}{2}}^{(2)}\left(z\right)=\mathrm{i}{\left(\frac{2}{\pi z}\right)}^{\frac{1}{2}}{\mathrm{e}}^{-\mathrm{i}z}.$$

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