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21: 10.60 Sums

… ►For further sums of series of spherical Bessel functions, or modified spherical Bessel functions, see §6.10(ii), Luke (1969b, pp. 55–58), Vavreck and Thompson (1984), Harris (2000), and Rottbrand (2000). … ►See also Watson (1944, Chapters 11 and 16).

22: Bibliography K

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Über die Wurzeln einiger Zylinderfunktionen und gewisser aus ihnen gebildeter Gleichungen. Zeitschrift für Mathematik und Physik 54, pp. 55–86 (German).

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External Links:

ZentralBlatt

Referenced by:

§10.21(x).

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Bernstein, Pick, Poisson and related integral expressions for Lambert $W$ . Integral Transforms Spec. Funct. 23 (11), pp. 817–829.

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ISSN 1065-2469, Document, Link, MathReview (Ross C. McPhedran), ZentralBlatt

Referenced by:

§4.13.

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Auxiliary table for the incomplete elliptic integrals. J. Math. Physics 27, pp. 11–36.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§19.12.

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Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11 (5), pp. 237–238.

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External Links:

Document, MathReview (C. Gilbert), ZentralBlatt

Referenced by:

§31.17(ii).

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Algorithm 327: Dilogarithm [S22]. Comm. ACM 11 (4), pp. 270–271.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§25.21(v).

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23: Bibliography P

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Optical properties of layer antiferromagnets with ${\mathrm{K}}_2{\mathrm{NiF}}_4$ structure. J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.

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External Links:

Document

Referenced by:

§19.35(ii).

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Numerical calculation of the generalized Fermi-Dirac integrals. Comput. Phys. Comm. 55 (2), pp. 127–136.

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External Links:

Document

Referenced by:

§25.18(i).

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Algorithm 28. Algorithm for the computation of Bessel function integrals. J. Comput. Appl. Math. 11 (1), pp. 119–137.

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ISSN 0377-0427, Document, ZentralBlatt

Referenced by:

§10.77(ix).

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24: Bibliography L

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Eine Verallgemeinerung der Sphäroidfunktionen. Arch. Math. 11, pp. 29–39.

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ISSN 0003-9268, Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§30.12.

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Higher monotonicity properties of certain Sturm-Liouville functions.. Acta Math. 109, pp. 55–73.

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ISSN 0001-5962, Document, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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Algorithm 244: Fresnel integrals. Comm. ACM 7 (11), pp. 660–661.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§7.25(iv).

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On the theory of Painlevé’s third equation. Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).

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Notes:

In Russian. English translation: Differential Equations 3(11), pp. 994–999

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.10(iii), §32.8(iii), §32.9(i), §32.9(ii).

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Algorithms for rational approximations for a confluent hypergeometric function. Utilitas Math. 11, pp. 123–151.

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External Links:

MathReview (F. Gotze), ZentralBlatt

Referenced by:

§13.31(iii).

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25: Bibliography B

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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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New “coherent” states associated with non-compact groups. Comm. Math. Phys. 21 (1), pp. 41–55.

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ISSN 0010-3616, MathReview (R. Mirman), ZentralBlatt

Referenced by:

§13.28(iii).

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Ramanujan’s theories of elliptic functions to alternative bases. Trans. Amer. Math. Soc. 347 (11), pp. 4163–4244.

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ISSN 0002-9947, FullText, MathReview (J. Borwein), ZentralBlatt

Referenced by:

§15.8(v), §20.11(iii).

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Vortices in Ginzburg-Landau Equations. In Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), pp. 11–19.

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External Links:

ISSN 1431-0643, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§17.17.

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Rainbow over Woolsthorpe Manor. Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).

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ISSN 0035-9149, Document, MathReview

Referenced by:

Sidebar 9.SB1.

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26: Bibliography D

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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.

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ISSN 0010-3640, Document, MathReview (D. S. Lubinsky), ZentralBlatt

Referenced by:

§18.32.

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Algorithm 322. F-distribution. Comm. ACM 11 (2), pp. 116–117.

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Notes:

Includes Algol program, maximum accuracy 10S. For certification see same journal 12(1969), p. 39

External Links:

ISSN 0001-0782, Document

Referenced by:

§8.28(iv).

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Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).

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Notes:

With an appendix by I. M. Krichever. In Russian. English translation: Russian Math. Surveys 36(1981), no. 2, pp. 11–92 (1982)

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ISSN 0042-1316, Document, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§21.1, §21.6(ii), §21.7(i), Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2, Ch.21, Notations T.

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Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.

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ISSN 0020-9910, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

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The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 11–29.

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ISSN 0003-9519, MathReview (Willard Parker), ZentralBlatt

Referenced by:

§8.17(i).

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27: 8.2 Definitions and Basic Properties

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8.2.11 $$\mathrm{\Gamma }(a,z{\mathrm{e}}^{\pm \pi \mathrm{i}})=\mathrm{\Gamma }\left(a\right)(1-z^a{\mathrm{e}}^{\pm \pi \mathrm{i}a}{\gamma }^{\ast }(a,-z)).$$

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\mathrm{\Gamma }(a,z)$: incomplete gamma function, ${\gamma }^{\ast }(a,z)$: incomplete gamma function, $z$: complex variable and $a$: parameter

Permalink:

http://dlmf.nist.gov/8.2.E11

Encodings:

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See also:

Annotations for §8.2(ii), §8.2 and Ch.8

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28: 36.5 Stokes Sets

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

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Symbols:

$x$: real parameter

Permalink:

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

Encodings:

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See also:

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

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29: Bibliography V

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Über die Riemann’sche Primzahlfunction. Math. Ann. 55, pp. 441–464 (German).

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ISSN 0025-5831; 1432-1807/e, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.12.

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30: Bibliography M

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On the computation of zeroes of $J_n(z)-i{J}_{n+1}(z)=0$ . Quart. Appl. Math. 55 (4), pp. 623–633.

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ISSN 0033-569X, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(ix).

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Rational solutions of the Painlevé VI equation. J. Phys. A 34 (11), pp. 2281–2294.

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ISSN 0305-4470, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.8(vi).

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On the roots of the Bessel and certain related functions. Ann. of Math. 9 (1-6), pp. 23–30.

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ISSN 0003-486X, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§10.21(x).

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Spheroidal eigenfunctions of the tidal equation. Phys. Rev. Lett. 73 (11), pp. 1557–1560.

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External Links:

ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

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Zeros of the function $A{i}^{\prime }(z)-\sigma Ai(z)$ . Differential Equations 11, pp. 797–811.

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External Links:

ZentralBlatt

Referenced by:

§9.9(i).

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