distribution function

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21: Bibliography Z

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Distribution of zeros of Gauss and Kummer hypergeometric functions. A semiclassical approach. Ann. Numer. Math. 2 (1-4), pp. 457–472.

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External Links:

ISSN 1021-2655, MathReview (B. D. Agrawal), ZentralBlatt

Referenced by:

§13.9(i), §15.13.

Encodings:

BibTeX

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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications. Dover, New York.

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Notes:

Reprint of 1965 McGraw-Hill Publication

External Links:

ISBN 0-486-65479-6, MathReview Entry

Referenced by:

§1.16(ix).

Encodings:

BibTeX

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22: 15.18 Physical Applications

§15.18 Physical Applications

►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). ►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).

23: 1.11 Zeros of Polynomials

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§1.11(ii) Elementary Properties

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

$z_1{z}_2\mathrm{\cdots }{z}_n={(-1)}^n{a}_0/a_n.$

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1.11.23 $$\sqrt[n]{R}\left(\cos \left(\frac{\alpha +2k\pi }{n}\right)+\mathrm{i}\sin \left(\frac{\alpha +2k\pi }{n}\right)\right),$$

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\cos z$: cosine function, $\mathrm{i}$: imaginary unit, $\sin z$: sine function, $k$: integer, $n$: nonnegative integer and $R$: radius

Permalink:

http://dlmf.nist.gov/1.11.E23

Encodings:

pMML, png, TeX

See also:

Annotations for §1.11(iv), §1.11 and Ch.1

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24: 10.73 Physical Applications

… ►The analysis of the current distribution in circular conductors leads to the Kelvin functions $\mathrm{ber}x$, $\mathrm{bei}x$, $\ker x$, and $\mathrm{kei}x$. …

25: 1.4 Calculus of One Variable

… ►Delta distributions and Dirac $\delta$-functions are discussed in §§1.16(iii), 1.16(iv) and 1.17. …

26: Bibliography H

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On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.

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External Links:

FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§9.13(i).

Encodings:

BibTeX

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27: Bibliography W

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The distribution of the zeros of Jacobian elliptic functions with respect to the parameter $k$ . Comput. Methods Funct. Theory 9 (2), pp. 579–591.

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External Links:

ISSN 1617-9447, MathReview (M. K. Jain), ZentralBlatt

Referenced by:

§22.4(i).

Encodings:

BibTeX

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28: Bibliography K

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Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution. Justus von Liebig Verlag, Darmstadt (German, English).

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Notes:

In cooperation with W. Rudert

External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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29: 11.12 Physical Applications

… ►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). …

30: Bibliography F

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Notes:

The “Freely Distributable LIBM” package provides implementations of standard elementary functions plus a few higher functions, e.g. gamma. Double precision, maximum accuracy 20S. Developed by Sun Microsystems.

External Links:

GAMS (package FDLIBM)

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

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