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21—30 of 151 matching pages

21: 24.20 Tables

… ►Wagstaff (1978) gives complete prime factorizations of $N_n$ and $E_n$ for $n=20(2)60$ and $n=8(2)42$, respectively. …

22: Bibliography N

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Modern Computing Methods. 2nd edition, Notes on Applied Science, No. 16, Her Majesty’s Stationery Office, London.

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External Links:

MathReview (A. S. Householder), ZentralBlatt

Referenced by:

§3.8(iv).

Encodings:

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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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External Links:

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

Referenced by:

§28.26(ii).

Encodings:

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

Encodings:

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Mathematical Approximation of Special Functions. Nova Science Publishers Inc., Commack, NY.

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Notes:

Ten papers on Chebyshev expansions

External Links:

ISBN 1-56072-052-2, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.76(ii), §10.76(ii), §10.76(ii), §10.76(iii), 2nd item.

Encodings:

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

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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:

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23: Bernard Deconinck

… ►He received his Diploma in Engineering Physics from the University of Ghent, Belgium. …In addition, he has spent time at the University of Alberta, the Mathematical Sciences Research Institute in Berkeley, California, and Colorado State University. …

24: Bibliography P

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

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Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

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Notes on Introductory Combinatorics. Progress in Computer Science, Vol. 4, Birkhäuser Boston Inc., Boston, MA.

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External Links:

ISBN 0-8176-3123-2; 0-8176-3170-4, MathReview (Bernard M. E. Moret), ZentralBlatt

Referenced by:

§26.18.

Encodings:

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Voronoi type congruences for Bernoulli numbers. In Voronoi’s Impact on Modern Science. Book I, P. Engel and H. Syta (Eds.),

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External Links:

ZentralBlatt

Referenced by:

§24.10(iii).

Encodings:

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Integrals and Series: Elementary Functions, Vol. 1. Gordon & Breach Science Publishers, New York.

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Notes:

Translated from the Russian and with a preface by N. M. Queen. Table errata: Math. Comp. v. 66 (1997), no. 220, pp. 1765–1766, Math. Comp. v. 65 (1996), no. 215, pp. 1380–1381 .

External Links:

ISBN 2-88124-097-6, MathReview, ZentralBlatt

Referenced by:

§1.14(viii), §1.4(iv), §1.8(v), §24.7(iii), §4.10(iii), §4.11, §4.26(v), §4.27, §4.40(v), §4.41.

Encodings:

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Integrals and Series: Special Functions, Vol. 2. Gordon & Breach Science Publishers, New York.

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Notes:

A second edition was published in 1988. Table errata: Math. Comp. v. 65 (1996), no. 215, pp. 1382–1383

External Links:

ISBN 2-88124-097-6, MathReview, ZentralBlatt

Referenced by:

§1.14(viii), §1.4(iv), §10.22(vi), §10.23(iv), §10.43(v), §10.43(vi), §10.44(iv), §10.60(iv), §10.71(iii), §12.12, §12.13(ii), §18.17(ix), §18.18(ix), §25.7, §25.8, §5.13, §6.14(iii), §6.15, §7.14(iii), §7.15, §8.14, §8.15.

Encodings:

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25: 6.20 Approximations

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Cody and Thacher (1968) provides minimax rational approximations for $E_1\left(x\right)$, with accuracies up to 20S.

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Cody and Thacher (1969) provides minimax rational approximations for $\mathrm{Ei}\left(x\right)$, with accuracies up to 20S.

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MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions $\mathrm{f}$ and $\mathrm{g}$, with accuracies up to 20S.

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26: 13.30 Tables

… ►

Zhang and Jin (1996, pp. 411–423) tabulates $M(a,b,x)$ and $U(a,b,x)$ for $a=-5(.5)5$, $b=0.5(.5)5$, and $x=0.1,1,5,10,20,30$, 8S (for $M(a,b,x)$) and 7S (for $U(a,b,x)$).

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27: 28.16 Asymptotic Expansions for Large $q$

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28.16.1 $${\lambda }_{\nu }\left(h^2\right)\sim -2h^2+2sh-\frac{1}{8}(s^2+1)-\frac{1}{2^{7}h}(s^3+3s)-\frac{1}{2^{12}{h}^2}(5s^4+34s^2+9)-\frac{1}{2^{17}{h}^3}(33s^5+410s^3+405s)-\frac{1}{2^{20}{h}^4}(63s^6+1260s^4+2943s^2+486)-\frac{1}{2^{25}{h}^5}(527s^7+15617s^5+69001s^3+41607s)+\mathrm{\cdots }.$$

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Symbols:

${\lambda }_{\nu +2n}\left(q\right)$: eigenvalues of Mathieu equation, $\sim$: Poincaré asymptotic expansion, $h$: parameter and $\nu$: complex parameter

Permalink:

http://dlmf.nist.gov/28.16.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §28.16 and Ch.28

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28: Bibliography B

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

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External Links:

Document

Referenced by:

§33.22(iv).

Encodings:

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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.

Encodings:

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Electromagnetic Scattering and its Applications. Applied Science Publishers, London.

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External Links:

ISBN 0-85334-955-X

Referenced by:

§10.73(i), §10.73(ii).

Encodings:

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Tablit͡sy Elliptic͡heskik͡h Integralov. Tom I. Mathematical tables of the Computing Center of the Academy of Sciences of the USSR, Izdat. Akad. Nauk SSSR, Moscow (Russian).

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Notes:

Reviewed in Math. Comp. v. 18(1964), pp. 676–677.

External Links:

MathReview (John Todd), ZentralBlatt

Referenced by:

§19.37(ii), §19.37(iii), §19.37(iii).

Encodings:

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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.

Encodings:

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29: Bibliography G

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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 (1), pp. 21–62.

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Notes:

For remark see same journal 24(1998), p. 355.

External Links:

Document, ISSN 0098-3500, GAMS (module 726; package TOMS), ZentralBlatt

Referenced by:

2nd item, §3.5(v), §3.5(v).

Encodings:

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

External Links:

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

Referenced by:

3rd item, §10.77(ix).

Encodings:

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Lectures on Integration of the Equations of Motion of a Rigid Body About a Fixed Point. Translated from the Russian by J. Shorr-Kon, Office of Technical Services, U. S. Department of Commerce, Washington, D.C..

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Notes:

Published for the National Science Foundation by the Israel Program for Scientific Translations, 1960.

External Links:

MathReview, ZentralBlatt

Referenced by:

§22.19(iv).

Encodings:

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Handbook of Combinatorics. Vols. 1, 2. Elsevier Science B.V., Amsterdam.

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External Links:

ISBN 0-444-88002-X, MathReview, ZentralBlatt

Referenced by:

§26.19, §26.20, Ch.26.

Encodings:

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Concrete Mathematics: A Foundation for Computer Science. 2nd edition, Addison-Wesley Publishing Company, Reading, MA.

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External Links:

ISBN 0-201-55802-5, MathReview (Volker Strehl), ZentralBlatt

Referenced by:

§1.2(i), §1.2(ii), §1.2(iii), §24.15(ii), §24.17(i), §26.1, §26.1, §26.14(i), §26.14(ii), §26.14(iii), §26.14(iv), §26.8(iii), §26.8(iv), §26.8(v), Notations, Notations.

Encodings:

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30: 7.24 Approximations

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Cody (1969) provides minimax rational approximations for $\mathrm{erf}x$ and $\mathrm{erfc}x$. The maximum relative precision is about 20S.

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Cody et al. (1970) gives minimax rational approximations to Dawson’s integral $F\left(x\right)$ (maximum relative precision 20S–22S).

…