Airy%20function

SearchAdvancedHelp

(0.004 seconds)

11—20 of 23 matching pages

11: Bibliography C

… ►

A dispersion analysis for difference schemes: Tables of generalized Airy functions. Math. Comp. 32 (144), pp. 1163–1170.

ⓘ

External Links:

ISSN 0025-5718, FullText, MathReview (Philip Brenner), ZentralBlatt

Referenced by:

§9.13(ii).

Encodings:

BibTeX

… ►

Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

ⓘ

External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

… ►

Efficient and accurate computation of the incomplete Airy functions. Radio Science 28 (4), pp. 441–457.

ⓘ

External Links:

ISSN 0048-6604, Document

Referenced by:

§9.14.

Encodings:

BibTeX

… ►

On the asymptotic expansion of Airy’s integral. Proc. Glasgow Math. Assoc. 6, pp. 113–115.

ⓘ

External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

(9.5.7), §9.5(ii).

Encodings:

BibTeX

… ►

Numerical evaluation of Airy functions with complex arguments. J. Comput. Phys. 99 (1), pp. 106–114.

ⓘ

External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt

Referenced by:

4th item, 1st item.

Encodings:

BibTeX

…

12: Bibliography S

… ►

Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

Encodings:

BibTeX

… ►

Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

ⓘ

External Links:

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

Referenced by:

§28.8(iv).

Encodings:

BibTeX

… ►

The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.

ⓘ

External Links:

ISSN 0253-424X, MathReview

Referenced by:

§9.10(v).

Encodings:

BibTeX

… ►

Tables of Airy Functions and Special Confluent Hypergeometric Functions. Pergamon Press, New York.

ⓘ

Notes:

Translated from the Russian by D. G. Fry

External Links:

MathReview (W. F. Freiberger), ZentralBlatt

Referenced by:

(9.13.19), (9.13.20), (9.13.21), §9.13(i), 1st item.

Encodings:

BibTeX

… ►

A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

ⓘ

Notes:

For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.

External Links:

Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

…

13: Bibliography

… ►

Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

ⓘ

External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

BibTeX

… ►

On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Phil. Soc. 6, pp. 379–402.

ⓘ

Referenced by:

§9.16, §9.16.

Encodings:

BibTeX

… ►

Integrals involving Airy functions. J. Phys. A 19 (13), pp. 2663–2665.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

(9.11.11), (9.11.12), (9.11.13), (9.11.14), §9.11(iv).

Encodings:

BibTeX

►

Integrals of products of Airy functions. J. Phys. A 10 (4), pp. 485–490.

ⓘ

External Links:

Document, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

(9.11.10), (9.11.5), (9.11.6), (9.11.7), (9.11.8), (9.11.9), §9.11(iv), §9.11(iv).

Encodings:

BibTeX

… ►

Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

Encodings:

BibTeX

…

14: 12.10 Uniform Asymptotic Expansions for Large Parameter

… ►The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions (§2.8(iii)). … ►

§12.10(vii) Negative $a$, . Expansions in Terms of Airy Functions

… ►

Modified Expansions

… ►

§12.10(viii) Negative $a$, . Expansions in Terms of Airy Functions

… ►

15: 36.5 Stokes Sets

… ►

$K=1$. Airy Function

… ►

36.5.4 $$80x^5-40x^4-55x^3+5x^2+20x-1=0,$$

ⓘ

Symbols:

$x$: real parameter

Permalink:

http://dlmf.nist.gov/36.5.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36

… ►

36.5.7 $$X=\frac{9}{20}+20u^4-\frac{Y^2}{20u^2}+6u^2\mathrm{sign}\left(z\right),$$

ⓘ

Symbols:

$\mathrm{sign}x$: sign of, $z$: real parameter, $X$: scaled coordinate and $Y$: scaled coordinate

Permalink:

http://dlmf.nist.gov/36.5.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36

…

16: Bibliography P

… ►

Tables of Digamma and Trigamma Functions. In Tracts for Computers, No. 1, K. Pearson (Ed.),

ⓘ

External Links:

ZentralBlatt

Referenced by:

§5.1, Notations F.

Encodings:

BibTeX

… ►

Exponential asymptotics of the Mittag-Leffler function. Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview (Roderick Wong), ZentralBlatt

Referenced by:

§10.46.

Encodings:

BibTeX

… ►

Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX

… ►

Inequalities for the zeros of the Airy functions. SIAM J. Math. Anal. 22 (1), pp. 260–267.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview, ZentralBlatt

Referenced by:

§9.9(iv).

Encodings:

BibTeX

… ►

Algorithm 498: Airy functions using Chebyshev series approximations. ACM Trans. Math. Software 1 (4), pp. 372–379.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 498; package TOMS), ZentralBlatt

Referenced by:

1st item, 4th item.

Encodings:

BibTeX

…

17: Software Index

… ► ►►►

	Open Source													With Book						Commercial
…
20 Theta Functions
…

►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

… ►The following are web-based software repositories with significant holdings in the area of special functions. …

18: Bibliography B

… ►

Zeros of generalized Airy functions. Mathematika 32 (1), pp. 104–117.

ⓘ

External Links:

ISSN 0025-5793, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§9.13(ii).

Encodings:

BibTeX

… ►

A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

ⓘ

Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

Encodings:

BibTeX

… ►

A short table of the functions ${\mathrm{Ki}}_n(x)$, from $n=1$ to $n=16$ . Phil. Mag. Series 7 20, pp. 343–347.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§10.43(iii), 2nd item.

Encodings:

BibTeX

… ►

Bessel functions and modular relations of higher type and hyperbolic differential equations. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

ⓘ

External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§35.5(i).

Encodings:

BibTeX

…

19: 3.8 Nonlinear Equations

§3.8 Nonlinear Equations

… ►

§3.8(v) Zeros of Analytic Functions

… ►For an example involving the Airy functions, see Fabijonas and Olver (1999). … ►Consider $x=20$ and $j=19$. We have $p^{\prime }(20)=19!$ and $a_{19}=1+2+\mathrm{\cdots }+20=210$. …

20: 36.2 Catastrophes and Canonical Integrals

… ► ${\mathrm{\Psi }}_1$ is related to the Airy function (§9.2): ►

36.2.13 $${\mathrm{\Psi }}_1\left(x\right)=\frac{2\pi }{3^{1/3}}\mathrm{Ai}\left(\frac{x}{3^{1/3}}\right).$$

ⓘ

Symbols:

$\mathrm{Ai}\left(z\right)$: Airy function, ${\mathrm{\Psi }}_K\left(𝐱\right)$: canonical integral function, $\pi$: the ratio of the circumference of a circle to its diameter and $x$: real parameter

Referenced by:

§36.2(ii)

Permalink:

http://dlmf.nist.gov/36.2.E13

Encodings:

pMML, png, TeX

See also:

Annotations for §36.2(ii), §36.2 and Ch.36

… ► … ►For the Bessel function $J$ see §10.2(ii). … ►Addendum: For further special cases see §36.2(iv) …