general properties

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11: Bibliography G

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Generalized Functions. Vol. 1: Properties and Operations. Academic Press, New York.

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Notes:

Translated from the Russian by Eugene Saletan. A paperbound reprinting by the same publisher appeared in 1977

External Links:

MathReview, ZentralBlatt

Referenced by:

§2.6(i).

Encodings:

BibTeX

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Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. Comput. Phys. Comm. 136 (3), pp. 294–309.

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Notes:

Double-precision Fortran, maximum accuracy 20D

External Links:

Document, Code, ZentralBlatt

Referenced by:

7th item.

Encodings:

BibTeX

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12: 14.29 Generalizations

§14.29 Generalizations

… ►are called Generalized Associated Legendre Functions. …For properties see Virchenko and Fedotova (2001) and Braaksma and Meulenbeld (1967). ►For inhomogeneous versions of the associated Legendre equation, and properties of their solutions, see Babister (1967, pp. 252–264).

13: 2.1 Definitions and Elementary Properties

… ►As in §2.1(iv), generalized asymptotic expansions can also have uniformity properties with respect to parameters. …

14: Bibliography L

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Monotonicity properties of zeros of generalized Airy functions. Z. Angew. Math. Phys. 39 (2), pp. 267–271.

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External Links:

ISSN 0044-2275, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§9.13(i).

Encodings:

BibTeX

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15: 8.21 Generalized Sine and Cosine Integrals

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8.21.2 $$\mathrm{Ci}(a,z)\pm \mathrm{i}\mathrm{Si}(a,z)={\mathrm{e}}^{\pm \frac{1}{2}\pi \mathrm{i}a}\gamma (a,z{\mathrm{e}}^{\mp \frac{1}{2}\pi \mathrm{i}}).$$

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Defines:

$\mathrm{Ci}(a,z)$: generalized cosine integral and $\mathrm{Si}(a,z)$: generalized sine integral

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\gamma (a,z)$: incomplete gamma function, $z$: complex variable and $a$: parameter

Referenced by:

§8.21(ii)

Permalink:

http://dlmf.nist.gov/8.21.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §8.21(i), §8.21 and Ch.8

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16: 4.37 Inverse Hyperbolic Functions

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4.37.6 $$\mathrm{Arccoth}z=\mathrm{Arctanh}\left(1/z\right).$$

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Defines:

$\mathrm{Arccoth}z$: general inverse hyperbolic cotangent function

Symbols:

$\mathrm{Arctanh}z$: general inverse hyperbolic tangent function and $z$: complex variable

Permalink:

http://dlmf.nist.gov/4.37.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §4.37(i), §4.37 and Ch.4

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17: 8.19 Generalized Exponential Integral

§8.19 Generalized Exponential Integral

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§8.19(ii) Graphics

… ►For properties and numerical tables see Milgram (1985), and also (when $p=1$) MacLeod (2002b). … ►

§8.19(ix) Inequalities

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§8.19(xi) Further Generalizations

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18: 4.2 Definitions

… ►With this definition the general logarithm is given by … ►As a consequence, it has the advantage of extending regions of validity of properties of principal values. … ►

§4.2(ii) Logarithms to a General Base $a$

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§4.2(iii) The Exponential Function

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Powers with General Bases

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19: 16.23 Mathematical Applications

… ►These equations are frequently solvable in terms of generalized hypergeometric functions, and the monodromy of generalized hypergeometric functions plays an important role in describing properties of the solutions. …

20: 4.23 Inverse Trigonometric Functions

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4.23.6 $$\mathrm{Arccot}z=\mathrm{Arctan}\left(1/z\right).$$

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Defines:

$\mathrm{Arccot}z$: general arccotangent function

Symbols:

$\mathrm{Arctan}z$: general arctangent function and $z$: complex variable

A&S Ref:

4.4.8 (modified)

Permalink:

http://dlmf.nist.gov/4.23.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §4.23(i), §4.23 and Ch.4

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