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11: 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:

BibTeX

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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:

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.

Encodings:

BibTeX

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

Encodings:

BibTeX

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Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and Procrustes analysis. J. Multivariate Anal. 41 (2), pp. 314–337.

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External Links:

ISSN 0047-259X, Document, MathReview (A. L. Rukhin), ZentralBlatt

Referenced by:

§35.10, §35.9.

Encodings:

BibTeX

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12: 12.10 Uniform Asymptotic Expansions for Large Parameter

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12.10.33 $${𝖠}_{s+1}(\tau )=-4{\tau }^2{(\tau +1)}^2\frac{d}{d\tau }{𝖠}_s(\tau )-\frac{1}{4}{\int }_0^{\tau }\left(20u^2+20u+3\right){𝖠}_s(u)du,$$ $s=0,1,2,\mathrm{\dots }$,

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Defines:

${𝖠}_s(\tau )$: coefficients (locally)

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $dx$: differential of $x$ , $\int$: integral, $s$: nonnegative integer and $\tau$

Permalink:

http://dlmf.nist.gov/12.10.E33

Encodings:

pMML, png, TeX

See also:

Annotations for §12.10(vi), §12.10 and Ch.12

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$${𝖠}_1(\tau )=-\frac{1}{12}\tau (20{\tau }^2+30\tau +9),$$

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12.10.40 $$\varphi (\zeta )={\left(\frac{\zeta }{t^2-1}\right)}^{\frac{1}{4}}.$$

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Defines:

$\varphi (\zeta )$: function (locally)

Symbols:

$\zeta$: change of variable

Referenced by:

§12.10(vii)

Permalink:

http://dlmf.nist.gov/12.10.E40

Encodings:

pMML, png, TeX

See also:

Annotations for §12.10(vii), §12.10 and Ch.12

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12.10.41 $$t=1+w-\frac{1}{10}{w}^2+\frac{11}{350}{w}^3-\frac{823}{63000}{w}^4+\frac{\mathrm{1\hspace{0.33em}50653}}{\mathrm{242\hspace{0.33em}55000}}{w}^5+\mathrm{\cdots },$$

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter and $\zeta$: change of variable

Referenced by:

§12.11(iii), §12.11(iii)

Permalink:

http://dlmf.nist.gov/12.10.E41

Encodings:

pMML, png, TeX

See also:

Annotations for §12.10(vii), §12.10 and Ch.12

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12.10.45 $$\chi (\zeta )=\frac{{\varphi }^{\prime }(\zeta )}{\varphi (\zeta )}=\frac{1-2t{(\varphi (\zeta ))}^6}{4\zeta }.$$

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Defines:

$\chi (\zeta )$ (locally)

Symbols:

$\zeta$: change of variable and $\varphi (\zeta )$: function

Permalink:

http://dlmf.nist.gov/12.10.E45

Encodings:

pMML, png, TeX

See also:

Annotations for §12.10(vii), §12.10 and Ch.12

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13: 20.10 Integrals

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14: Bibliography K

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

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A vortex filament moving without change of form. J. Fluid Mech. 112, pp. 397–409.

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External Links:

ISSN 0022-1120, Document, MathReview, ZentralBlatt

Referenced by:

§19.35(ii).

Encodings:

BibTeX

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

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The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.

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External Links:

ISSN 1382-4090, Document, FullText, MathReview (José Luis López), ZentralBlatt

Referenced by:

§18.26(v), §18.26(v).

Encodings:

BibTeX

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15: 14.30 Spherical and Spheroidal Harmonics

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