.%E5%A8%81%E5%B0%BC%E6%96%AF%E8%B5%8C%E5%9C%BA%E3%80%8Ewn4.com%E3%80%8F%E6%BE%B3%E9%97%A8%E5%A8%81%E5%B0%BC%E6%96%AF%E8%B5%8C%E5%9C%BA.%E5%A8%81%E5%B0%BC%E6%96%AF%E7%BA%BF%E4%B8%8A%E8%B5%8C%E5%9C%BA.%E7%9C%9F%E7%9A%84%E5%A8%81%E5%B0%BC%E6%96%AF%E8%B5%8C%E5%9C%BA.%E5%A8%81%E5%B0%BC%E6%96%AF%E5%A8%B1%E4%B9%90.%E5%A8%81%E5%B0%BC%E6%96%AF%E7%9C%9F%E4%BA%BA.%E5%A8%81%E5%B0%BC%E6%96%AF%E6%A3%8B%E7%89%8C-w6n2c9o.2022%E5%B9%B411%E6%9C%8829%E6%97%A54%E6%97%B651%E5%88%8618%E7%A7%92.q000s0soc.com

SearchAdvancedHelp

(0.072 seconds)

21—30 of 715 matching pages

21: Bibliography F

… ►

Tables of Elliptic Integrals of the First, Second, and Third Kind. Technical report Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.

ⓘ

Notes:

Reviewed in Math. Comp. v. 1919(1965)509. Table erratum: Math. Comp. v. 20 (1966), no. 96, pp. 639-640.

Referenced by:

§19.37(ii), §19.37(ii), §19.37(iii), §19.37(iii), §19.37(iii).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

ISSN 0001-0782, Document

Referenced by:

§5.24(ii).

Encodings:

BibTeX

… ►

Diffraction of radio waves around the earth’s surface. Acad. Sci. USSR. J. Phys. 9, pp. 255–266.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§9.1, Notations U, Notations V.

Encodings:

BibTeX

… ►

Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions. In Progress in Optics, E. Wolf (Ed.), Vol. 9, pp. 311–407.

ⓘ

Referenced by:

§30.15(i), §30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

Encodings:

BibTeX

… ►

Series expansions of symmetric elliptic integrals. Math. Comp. 81 (278), pp. 957–990.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§20.7(ii), §20.7(ii).

Encodings:

BibTeX

…

22: Bibliography B

… ►

The generating function of Jacobi polynomials. J. London Math. Soc. 13, pp. 8–12.

ⓘ

External Links:

ISSN 0024-6107; 1469-7750/e, Document, ZentralBlatt

Referenced by:

§18.18(vii).

Encodings:

BibTeX

… ►

Asymptotic behavior of the Pollaczek polynomials and their zeros. Stud. Appl. Math. 96, pp. 307–338.

ⓘ

External Links:

ISSN 0022-2526, MathReview (Harold Exton), ZentralBlatt

Referenced by:

§18.35(iii).

Encodings:

BibTeX

… ►

Algorithm 524: MP, A Fortran multiple-precision arithmetic package [A1]. ACM Trans. Math. Software 4 (1), pp. 71–81.

ⓘ

External Links:

ISSN 0098-3500, Document, Remark. GAMS (module 524; package TOMS)

Referenced by:

3rd item, 1st item, 1st item, 1st item, 3rd item, 1st item, 1st item.

Encodings:

BibTeX

… ►

Irregular primes and cyclotomic invariants to 12 million. J. Symbolic Comput. 31 (1-2), pp. 89–96.

ⓘ

Notes:

Computational algebra and number theory (Milwaukee, WI, 1996)

External Links:

ISSN 0747-7171, Document, MathReview (Xavier-François Roblot), ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

… ►

The determination of phases and amplitudes of wave functions. Proc. Phys. Soc. 81 (3), pp. 442–452.

ⓘ

External Links:

Document

Referenced by:

§33.23(vii).

Encodings:

BibTeX

…

23: Bibliography W

… ►

Extension of a quadratic transformation due to Whipple with an application. Adv. Difference Equ., pp. 2013:157, 8.

ⓘ

External Links:

ISSN 1687-1847, Document, FullText, MathReview (Daniele Ritelli), ZentralBlatt

Referenced by:

§16.6, §16.6.

Encodings:

BibTeX

… ►

A note on the trinomial analogue of Bailey’s lemma. J. Combin. Theory Ser. A 81 (1), pp. 114–118.

ⓘ

External Links:

ISSN 0097-3165, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX

… ►

Asymptotic approximations for certain $6$-$j$ and $9$-$j$ symbols. J. Phys. A 32 (39), pp. 6901–6902.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§34.8, §34.8.

Encodings:

BibTeX

►

Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.

ⓘ

External Links:

Online edition, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§11.12.

Encodings:

BibTeX

… ►

Upon systems of recursions which obtain among the quotients of the Padé table. Numer. Math. 8 (3), pp. 264–269.

ⓘ

External Links:

ISSN 0029-599X, Document, MathReview (F. L. Bauer), ZentralBlatt

Referenced by:

§3.11(iv).

Encodings:

BibTeX

24: 11.11 Asymptotic Expansions of Anger–Weber Functions

… ►Let $F_0(\nu )=G_0(\nu )=1$, and for $k=1,2,3,\mathrm{\dots }$, … ►

$a_2(\lambda )={\displaystyle \frac{9{\lambda }^2-\lambda }{24{(1+\lambda )}^7}},$

… ►

$b_2(\lambda )={\displaystyle \frac{4+300{\lambda }^2+81{\lambda }^4}{864{(1-{\lambda }^2)}^{13/4}}}$ .

… ►When $\nu$ is real and positive, all of (11.11.10)–(11.11.17) can be regarded as special cases of two asymptotic expansions given in Olver (1997b, pp. 352–360) for ${𝐀}_{-\nu }\left(\lambda \nu \right)$ as $\nu \to +\mathrm{\infty }$, one being uniform for , and the other being uniform for $\lambda \ge 1$. (Note that Olver’s definition of ${𝐀}_{\nu }\left(z\right)$ omits the factor $1/\pi$ in (11.10.4).) …

25: Bibliography G

… ►

Basic Hypergeometric Series. Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge.

ⓘ

Notes:

A revised and updated edition, with three new chapters, was published in 2004 by Cambridge University Press (Encyclopedia of Mathematics and its Applications, vol. 96).

External Links:

ISBN 0-521-35049-2, MathReview (Shaun Cooper), ZentralBlatt

Referenced by:

(17.9.3), Erratum (V1.0.23) for Equation (17.9.3).

Encodings:

BibTeX

►

Basic Hypergeometric Series. Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.

ⓘ

Notes:

With a foreword by Richard Askey

External Links:

ISBN 0-521-83357-4, MathReview (Shaun Cooper), ZentralBlatt

Referenced by:

§17.1, §17.1, §17.10, (17.11.1), (17.11.2), (17.11.3), §17.13, §17.16, (17.4.5), (17.4.6), (17.4.7), (17.4.8), §17.4(i), §17.5, §17.6(i), §17.6(ii), §17.6(iii), §17.6(iv), §17.6(v), §17.7(i), §17.7(ii), §17.7(iii), §17.8, (17.9.3), §17.9(i), §17.9(ii), §17.9(iii), Ch.17, §18.27(i), §18.27(i), §18.27(ii), §18.27(iii), §18.27(iv), (18.28.24), (18.28.25), §18.28(i), §18.28(ii), §18.28(v), §18.28(viii), §26.19, Erratum (V1.0.10) for Section 17.1, Erratum (V1.0.23) for Equation (17.9.3).

Encodings:

BibTeX

… ►

Algorithm 236: Bessel functions of the first kind. Comm. ACM 7 (8), pp. 479–480.

ⓘ

Notes:

For certification see same journal 8(1965), pp. 105–106, for remark see ACM Trans. Math. Software, 1(1975), pp. 282–284. Includes Algol program, maximum accuracy: 11D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§10.77(iii).

Encodings:

BibTeX

►

Algorithm 259: Legendre functions for arguments larger than one. Comm. ACM 8 (8), pp. 488–492.

ⓘ

Notes:

Variable-precision Algol. For remark see ACM Trans. Math. Software 3(2) (1977), p. 204–205

External Links:

ISSN 0001-0782, Document

Referenced by:

§14.34(ii).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

MathReview (H. O. Pollak), ZentralBlatt

Referenced by:

§5.6(i), §6.8, §7.8, §8.10.

Encodings:

BibTeX

…

26: 1.10 Functions of a Complex Variable

… ►Let $C$ be a simple closed contour consisting of a segment $\mathrm{𝐴𝐵}$ of the real axis and a contour in the upper half-plane joining the ends of $\mathrm{𝐴𝐵}$. Also, let $f(z)$ be analytic within $C$, continuous within and on $C$, and real on $\mathrm{𝐴𝐵}$. … ►If $f(z)$ is analytic within a simple closed contour $C$, and continuous within and on $C$—except in both instances for a finite number of singularities within $C$—then …Here and elsewhere in this subsection the path $C$ is described in the positive sense. … ►If the singularities within $C$ are poles and $f(z)$ is analytic and nonvanishing on $C$, then …

27: 12.14 The Function $W(a,x)$

… ►This equation is important when $a$ and $z$ $(=x)$ are real, and we shall assume this to be the case. … ►For the modulus functions $\tilde{F}(a,x)$ and $\tilde{G}(a,x)$ see §12.14(x). … ►the branch of $\mathrm{ph}$ being zero when $a=0$ and defined by continuity elsewhere. … ►Other expansions, involving $\cos \left(\frac{1}{4}{x}^2\right)$ and $\sin \left(\frac{1}{4}{x}^2\right)$, can be obtained from (12.4.3) to (12.4.6) by replacing $a$ by $-\mathrm{i}a$ and $z$ by $x{\mathrm{e}}^{\pi \mathrm{i}/4}$; see Miller (1955, p. 80), and also (12.14.15) and (12.14.16). … ►Airy-type uniform asymptotic expansions can be used to include either one of the turning points $\pm 1$. …

28: 3.5 Quadrature

… ►where $h=b-a$, $f\in C^2[a,b]$, and . … ►If in addition $f$ is periodic, $f\in C^k(ℝ)$, and the integral is taken over a period, then … ►Let $h=\frac{1}{2}(b-a)$ and $f\in C^4[a,b]$. … ►For further information, see Mason and Handscomb (2003, Chapter 8), Davis and Rabinowitz (1984, pp. 74–92), and Clenshaw and Curtis (1960). … ►For $C^{\mathrm{\infty }}$ functions Gauss quadrature can be very efficient. …

29: Bibliography C

… ►

Elliptic integrals of the first kind. SIAM J. Math. Anal. 8 (2), pp. 231–242.

ⓘ

External Links:

Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§19.29(iii).

Encodings:

BibTeX

… ►

Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.

ⓘ

External Links:

MathReview (I. I. Hirschman, Jr.), ZentralBlatt

Referenced by:

§12.16.

Encodings:

BibTeX

… ►

Remarks on the full asymptotic expansion of Feynman parametrized integrals. Lett. Nuovo Cimento (2) 13 (8), pp. 310–312.

ⓘ

External Links:

MathReview (R. A. Askey)

Referenced by:

§2.3(iii).

Encodings:

BibTeX

►

Coulomb phase shift. American Journal of Physics 47 (8), pp. 683–684.

ⓘ

External Links:

Document

Referenced by:

§5.20.

Encodings:

BibTeX

… ►

Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives. Chem. Phys. Lett. 81 (2), pp. 306–310.

ⓘ

External Links:

ISSN 0009-2614, Document, MathReview (J. S. Joel)

Referenced by:

§36.14(iii).

Encodings:

BibTeX

…

30: 17.7 Special Cases of Higher ${}_r{}^{}\varphi _s^{}$ Functions

… ►

$q$-Analog of Bailey’s ${}_2{}^{}F_1^{}\left(-1\right)$ Sum

… ►

$q$-Analog of Gauss’s ${}_2{}^{}F_1^{}\left(-1\right)$ Sum

… ►

$q$-Analog of Dixon’s ${}_3{}^{}F_2^{}\left(1\right)$ Sum

… ►

Gasper–Rahman $q$-Analog of Watson’s ${}_3{}^{}F_2^{}$ Sum

… ►

Bailey’s Nonterminating Extension of Jackson’s ${}_8{}^{}\varphi _7^{}$ Sum

…