gamma%20function

SearchAdvancedHelp

(0.005 seconds)

11—20 of 34 matching pages

11: Bibliography D

… ►

Computation of the incomplete gamma function ratios and their inverses. ACM Trans. Math. Software 12 (4), pp. 377–393.

ⓘ

External Links:

ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

§8.12, §8.25(iii).

Encodings:

BibTeX

►

Algorithm 654: Fortran subroutines for computing the incomplete gamma function ratios and their inverses. ACM Trans. Math. Software 13 (3), pp. 318–319.

ⓘ

Notes:

Single-precision Fortran, maximum accuracy 14D.

External Links:

ISSN 0098-3500, Document, GAMS (module 654; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

ⓘ

Notes:

For a numerical error in one of the zeros see Amos (1985).

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

… ►

On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function. Methods Appl. Anal. 5 (3), pp. 223–247.

ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (John G. Stalker), ZentralBlatt

Referenced by:

§8.12.

Encodings:

BibTeX

… ►

Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

ⓘ

Notes:

(This reference has several typographical errors.)

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

Encodings:

BibTeX

…

12: 11.6 Asymptotic Expansions

… ►

§11.6(i) Large $|z|$, Fixed $\nu$

… ►where $\gamma$ is Euler’s constant (§5.2(ii)). ►

§11.6(ii) Large $|\nu |$, Fixed $z$

… ► … ►Here …

13: 9.7 Asymptotic Expansions

§9.7 Asymptotic Expansions

… ►Lastly, for $x>0$ we define … ►Numerical values of $\chi (n)$ are given in Table 9.7.1 for $n=1(1)20$ to 2D. … ►

§9.7(iii) Error Bounds for Real Variables

… ►

14: Bibliography

… ►

Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. 50 (4), pp. 419–428.

ⓘ

External Links:

ISSN 0029-599X, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§8.25(ii).

Encodings:

BibTeX

… ►

A harmonic mean inequality for the gamma function. J. Comput. Appl. Math. 87 (2), pp. 195–198.

ⓘ

Notes:

For corrigendum see same journal v. 90 (1998), no. 2, p. 265

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§5.6(i).

Encodings:

BibTeX

►

On some inequalities for the incomplete gamma function. Math. Comp. 66 (218), pp. 771–778.

ⓘ

External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§8.10.

Encodings:

BibTeX

… ►

Gamma function inequalities. Numer. Algorithms 49 (1-4), pp. 53–84.

ⓘ

External Links:

ISSN 1017-1398, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§5.6(i), §5.6(i).

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

…

15: 30.9 Asymptotic Approximations and Expansions

… ►

§30.9(i) Prolate Spheroidal Wave Functions

►As ${\gamma }^2\to +\mathrm{\infty }$, with $q=2(n-m)+1$, … ►The asymptotic behavior of ${\lambda }_n^m\left({\gamma }^2\right)$ and $a_{n,k}^m({\gamma }^2)$ as $n\to \mathrm{\infty }$ in descending powers of $2n+1$ is derived in Meixner (1944). …The behavior of ${\lambda }_n^m\left({\gamma }^2\right)$ for complex ${\gamma }^2$ and large $|{\lambda }_n^m\left({\gamma }^2\right)|$ is investigated in Hunter and Guerrieri (1982).

16: Bibliography B

… ►

Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

ⓘ

External Links:

Document

Referenced by:

§33.22(iv).

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

…

17: Bibliography N

… ►

On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

Encodings:

BibTeX

… ►

Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function. Appl. Anal. Discrete Math. 7 (1), pp. 161–179.

ⓘ

External Links:

ISSN 1452-8630, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§5.11(ii), §5.11(ii).

Encodings:

BibTeX

►

Generalization of Binet’s Gamma function formulas. Integral Transforms Spec. Funct. 24 (8), pp. 597–606.

ⓘ

External Links:

ISSN 1065-2469, Document, FullText, MathReview (Daniele Ritelli), ZentralBlatt

Referenced by:

§5.11(i), §5.11(i).

Encodings:

BibTeX

… ►

Inequalities and bounds for the incomplete gamma function. Results Math. 63 (3-4), pp. 1209–1214.

ⓘ

External Links:

ISSN 1422-6383, Document, FullText, MathReview (Pierpaolo Natalini), ZentralBlatt

Referenced by:

§8.10, §8.10.

Encodings:

BibTeX

… ►

A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

ⓘ

Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

External Links:

MathReview, ZentralBlatt

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

Encodings:

BibTeX

…

18: Bibliography P

… ►

Tablitsy nepolnoi gamma-funktsii. Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).

ⓘ

Notes:

In Russian. Translated title: Tables of the Incomplete Gamma Function.

External Links:

MathReview (John Todd)

Referenced by:

2nd item.

Encodings:

BibTeX

►

An asymptotic formula for the incomplete gamma function. Ž. Vyčisl. Mat. i Mat. Fiz. 5, pp. 118–121 (Russian).

ⓘ

Notes:

English translation in U.S.S.R. Computational Math. and Math. Phys. 5(1), pp. 162–166

External Links:

Document, MathReview (E. Lukacs), ZentralBlatt

Referenced by:

§8.11(iv).

Encodings:

BibTeX

… ►

Error bounds for the uniform asymptotic expansion of the incomplete gamma function. J. Comput. Appl. Math. 147 (1), pp. 215–231.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.12.

Encodings:

BibTeX

►

A uniform asymptotic expansion for the incomplete gamma function. J. Comput. Appl. Math. 148 (2), pp. 323–339.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

(8.11.6), §8.11(iii), (8.12.18), §8.12, §8.12, §8.12, Erratum (V1.0.16) for Equation (8.12.18).

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

…

19: 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. …

20: 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

… ►

Calculation of the gamma function by Stirling’s formula. Math. Comp. 25 (114), pp. 317–322.

ⓘ

External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§5.11(i), §5.11(ii).

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

… ►

Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

ⓘ

Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

Encodings:

BibTeX

…