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1: Bibliography I

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IEEE Standard for Floating-Point Arithmetic. The Institute of Electrical and Electronics Engineers, Inc..

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Notes:

IEEE Std 754-2008, Revision of IEEE Std 754-1985

External Links:

ISBN 978-0-7381-5753-5, Document

Referenced by:

§3.1(i).

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IEEE Standard for Interval Arithmetic: IEEE Std 1788-2015. The Institute of Electrical and Electronics Engineers, Inc..

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External Links:

ISBN 978-0-7381-9720-3, Document

Referenced by:

§3.1(ii), §3.1(ii), Erratum (V1.0.25) for Section 3.1.

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IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017. The Institute of Electrical and Electronics Engineers, Inc..

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External Links:

ISBN 978-1-5044-4602-0, Document

Referenced by:

§3.1(ii), §3.1(ii), Erratum (V1.0.25) for Section 3.1.

Encodings:

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IEEE International Standard for Information Technology—Microprocessor Systems—Floating-Point arithmetic: IEEE Std 754-2019. The Institute of Electrical and Electronics Engineers, Inc..

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Notes:

IEEE Std ISO/IEC/IEEE 60559, Revision of IEEE Std 754-1985

External Links:

ISBN 978-2-88912-566-1, Document

Referenced by:

Figure 3.1.1, Figure 3.1.1, §3.1(i), §3.1(i), Erratum (V1.0.25) for Section 3.1.

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The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

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2: Bibliography K

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The second Painlevé equation in electric probe theory. Some numerical solutions. Zh. Vychisl. Mat. Mat. Fiz. 38 (6), pp. 992–1000 (Russian).

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Notes:

In Russian. English translation: Comput. Math. Math. Phys. 38(1998), no. 6, pp. 950–958

External Links:

ISSN 0044-4669, MathReview, ZentralBlatt

Referenced by:

§32.17.

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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.

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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).

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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).

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Electromagnetic Fields and Relativistic Particles. International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.

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External Links:

ISBN 0-07-035264-X, MathReview (George Zipfel, Jr.)

Referenced by:

§1.17(ii), §10.73(ii).

Encodings:

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3: Wolter Groenevelt

… ►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. ►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. …

4: 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).

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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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Electromagnetic Fields and Interactions. Vol. I, Blaisdell, New York.

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Notes:

Replaces Abraham & Becker, Classical Theory of Electricity and Magnetism.

Referenced by:

§19.33(iii), §19.34.

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.

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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:

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5: 20 Theta Functions

Chapter 20 Theta Functions

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6: 19.33 Triaxial Ellipsoids

… ►If a conducting ellipsoid with semiaxes $a,b,c$ bears an electric charge $Q$, then the equipotential surfaces in the exterior region are confocal ellipsoids: …and the electric capacity $C=Q/V(0)$ is given by … ►Let a homogeneous magnetic ellipsoid with semiaxes $a,b,c$, volume $V=4\pi abc/3$, and susceptibility $\chi$ be placed in a previously uniform magnetic field $H$ parallel to the principal axis with semiaxis $c$. The external field and the induced magnetization together produce a uniform field inside the ellipsoid with strength $H/(1+L_c\chi )$, where $L_c$ is the demagnetizing factor, given in cgs units by … ►The same result holds for a homogeneous dielectric ellipsoid in an electric field. …

7: 31.15 Stieltjes Polynomials

… ►The system (31.15.2) determines the $z_k$ as the points of equilibrium of $n$ movable (interacting) particles with unit charges in a field of $N$ particles with the charges ${\gamma }_j/2$ fixed at $a_j$. … …

8: 33.22 Particle Scattering and Atomic and Molecular Spectra

§33.22 Particle Scattering and Atomic and Molecular Spectra

… ►With $\mathrm{e}$ denoting here the elementary charge, the Coulomb potential between two point particles with charges $Z_1\mathrm{e},Z_2\mathrm{e}$ and masses $m_1,m_2$ separated by a distance $s$ is $V(s)=Z_1{Z}_2{\mathrm{e}}^2/(4\pi {\epsilon }_{0}s)=Z_1{Z}_2\alpha \mathrm{\hslash }c/s$, where $Z_j$ are atomic numbers, ${\epsilon }_0$ is the electric constant, $\alpha$ is the fine structure constant, and $\mathrm{\hslash }$ is the reduced Planck’s constant. … ►

§33.22(iv) Klein–Gordon and Dirac Equations

►The relativistic motion of spinless particles in a Coulomb field, as encountered in pionic atoms and pion-nucleon scattering (Backenstoss (1970)) is described by a Klein–Gordon equation equivalent to (33.2.1); see Barnett (1981a). The motion of a relativistic electron in a Coulomb field, which arises in the theory of the electronic structure of heavy elements (Johnson (2007)), is described by a Dirac equation. …

9: 8 Incomplete Gamma and Related
Functions

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10: 28 Mathieu Functions and Hill’s Equation

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