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1: 8.26 Tables

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§8.26(ii) Incomplete Gamma Functions

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Khamis (1965) tabulates $P(a,x)$ for $a=0.05(.05)10(.1)20(.25)70$, $0.0001\le x\le 250$ to 10D.

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Pagurova (1963) tabulates $P(a,x)$ and $Q(a,x)$ (with different notation) for $a=0(.05)3$, $x=0(.05)1$ to 7D.

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Pearson (1965) tabulates the function $I(u,p)$ ($=P(p+1,u)$) for $p=-1(.05)0(.1)5(.2)50$, $u=0(.1)u_p$ to 7D, where $I(u,u_p)$ rounds off to 1 to 7D; also $I(u,p)$ for $p=-0.75(.01)-1$, $u=0(.1)6$ to 5D.

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§8.26(iii) Incomplete Beta Functions

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2: 8 Incomplete Gamma and Related
Functions

Chapter 8 Incomplete Gamma and Related Functions

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3: Bibliography G

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Algorithm 542: Incomplete gamma functions. ACM Trans. Math. Software 5 (4), pp. 482–489.

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Notes:

Single-precision Fortran.

External Links:

ISSN 0098-3500, Document, GAMS (module 542; package TOMS), ZentralBlatt

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2nd item.

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Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1), pp. 77–81.

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External Links:

MathReview (H. O. Pollak), ZentralBlatt

Referenced by:

§5.6(i), §6.8, §7.8, §8.10.

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BibTeX

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A computational procedure for incomplete gamma functions. ACM Trans. Math. Software 5 (4), pp. 466–481.

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External Links:

ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

§8.25(iv), §8.25(v).

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BibTeX

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The incomplete gamma functions since Tricomi. In Tricomi’s Ideas and Contemporary Applied Mathematics (Rome/Turin, 1997), Atti Convegni Lincei, Vol. 147, pp. 203–237.

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External Links:

FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

Ch.8.

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BibTeX

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A note on the recursive calculation of incomplete gamma functions. ACM Trans. Math. Software 25 (1), pp. 101–107.

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External Links:

ISSN 0098-3500, Document, MathReview Entry, ZentralBlatt

Referenced by:

§8.25(v).

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BibTeX

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4: 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.

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BibTeX

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Incomplete gamma functions for large values of their variables. Adv. in Appl. Math. 34 (3), pp. 467–485.

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ISSN 0196-8858, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§8.12.

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BibTeX

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An asymptotic expansion of the double gamma function. J. Approx. Theory 111 (2), pp. 298–314.

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ISSN 0021-9045, Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§5.17.

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BibTeX

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Algorithm 309. Gamma function with arbitrary precision. Comm. ACM 10 (8), pp. 511–512.

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External Links:

ISSN 0001-0782, Document

Referenced by:

§5.24(ii).

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BibTeX

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Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.

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Notes:

Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.

External Links:

ISSN 0001-0782, Document, Remark

Referenced by:

§8.28(ii).

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BibTeX

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5: Bibliography D

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

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External Links:

ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

§8.12, §8.25(iii).

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BibTeX

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

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Notes:

Single-precision Fortran, maximum accuracy 14D.

External Links:

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

Referenced by:

1st item.

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BibTeX

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

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External Links:

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

Referenced by:

§8.12.

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BibTeX

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Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function. Proc. Roy. Soc. London Ser. A 452, pp. 1331–1349.

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External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§2.8(vi), §8.12, §8.12.

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BibTeX

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Uniform asymptotic approximations for incomplete Riemann zeta functions. J. Comput. Appl. Math. 190 (1-2), pp. 339–353.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§8.22(ii).

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BibTeX

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6: Bibliography N

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

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

Referenced by:

§28.26(ii).

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BibTeX

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Uniform asymptotic expansion for the incomplete beta function. SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.

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External Links:

ISSN 1815-0659, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.18(ii), §8.18(ii), Erratum (V1.0.14) for Subsections 8.18(ii)–8.11(v).

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BibTeX

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The resurgence properties of the incomplete gamma function II. Stud. Appl. Math. 135 (1), pp. 86–116.

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External Links:

ISSN 0022-2526, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii).

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BibTeX

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The resurgence properties of the incomplete gamma function, I. Anal. Appl. (Singap.) 14 (5), pp. 631–677.

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External Links:

ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii), §8.11(v), §8.11(v), Erratum (V1.0.14) for Subsections 8.18(ii)–8.11(v).

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BibTeX

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

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External Links:

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

Referenced by:

§8.10, §8.10.

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BibTeX

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7: Bibliography B

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

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

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BibTeX

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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.

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External Links:

FullText, MathReview (J. C. P. Miller), ZentralBlatt

Referenced by:

§8.7.

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BibTeX

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

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

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BibTeX

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

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External Links:

Document, ZentralBlatt

Referenced by:

§10.43(iii), 2nd item.

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BibTeX

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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.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§35.5(i).

Encodings:

BibTeX

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8: Bibliography P

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

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Notes:

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

External Links:

MathReview (John Todd)

Referenced by:

2nd item.

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BibTeX

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

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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).

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BibTeX

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

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.12.

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BibTeX

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

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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).

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The asymptotic expansion of a generalised incomplete gamma function. J. Comput. Appl. Math. 151 (2), pp. 297–306.

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External Links:

ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt

Referenced by:

§8.16.

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BibTeX

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9: Bibliography C

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Asymptotics and closed form of a generalized incomplete gamma function. J. Comput. Appl. Math. 67 (2), pp. 371–379.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.16.

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BibTeX

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Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55 (1), pp. 99–124.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.16.

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BibTeX

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On a Class of Incomplete Gamma Functions with Applications. Chapman & Hall/CRC, Boca Raton, FL.

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External Links:

ISBN 1-58488-143-7, MathReview (R. K. Raina), ZentralBlatt

Referenced by:

§8.16.

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BibTeX

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Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.

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ISSN 0018-926X, Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§10.46.

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BibTeX

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

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External Links:

ISSN 0048-6604, Document

Referenced by:

§9.14.

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BibTeX

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10: Bibliography S

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

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External Links:

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

Referenced by:

§22.19(i), §22.20(vi).

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BibTeX

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

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External Links:

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

Referenced by:

§28.8(iv).

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BibTeX

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Algorithm AS 239. Chi-squared and incomplete gamma integral. Appl. Statist. 37 (3), pp. 466–473.

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Notes:

Double-precision Fortran.

External Links:

FullText, Code

Referenced by:

5th item.

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BibTeX

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Effective calculation of the incomplete gamma function for parameter values $\alpha =(2n+1)/2$, $n=0,\mathrm{\dots },5$ . Angew. Informatik 17, pp. 30–32.

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Notes:

Includes Fortran code.

External Links:

ZentralBlatt

Referenced by:

§8.28(ii).

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BibTeX

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

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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.

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BibTeX

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