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11: Bibliography K

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Heat conduction and diffusion in a fluid medium with a periodic flow. I. Determination of the wave transfer coefficient in a tube, slot, and canal. Akad. Nauk SSSR. Žurnal Eksper. Teoret. Fiz. 21, pp. 964–978.

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MathReview (N. A. Hall)

Referenced by:

§10.73(v).

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

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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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Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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A general addition theorem for spheroidal wave functions. SIAM J. Math. Anal. 4 (1), pp. 149–160.

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Document, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§30.10.

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Two new asymptotic methods in the theory of wave propagation in inhomogeneous media. Sov. Phys. Acoust. 14, pp. 1–17.

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ISSN 0038-562X

Referenced by:

§36.14(iv).

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12: 18.39 Applications in the Physical Sciences

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a) Spherical Radial Coulomb Wave Functions Expressed in terms of Laguerre OP’s

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c) Spherical Radial Coulomb Wave Functions

… ►The radial Coulomb wave functions $R_{n,l}(r)$, solutions of … ►

d) Radial Coulomb Wave Functions Expressed in Terms of the Associated Coulomb–Laguerre OP’s

… ►The Coulomb–Pollaczek polynomials provide alternate representations of the positive energy Coulomb wave functions of Chapter 33. …

13: Bibliography G

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Algorithm 292: Regular Coulomb wave functions. Comm. ACM 9 (11), pp. 793–795.

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ISSN 0001-0782, Document

Referenced by:

§33.26(ii).

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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.

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

Referenced by:

2nd item, §3.5(v), §3.5(v).

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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

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

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3rd item, §10.77(ix).

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Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt

Referenced by:

§18.38(iii).

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Algorithm 300: Coulomb wave functions. Comm. ACM 10 (4), pp. 244–245.

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Notes:

For remarks see same journal 12(1969), p. 692 and 16(1973), pp. 308-309 and for certification see same journal 12(1969), pp. 279-280.

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ISSN 0001-0782, Document

Referenced by:

§33.26(ii).

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14: Bibliography L

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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

Referenced by:

§4.13, 2nd item, §4.48(iv).

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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Microwave specific attenuation by oblate spheroidal raindrops: An exact analysis of TCS’s in terms of spheroidal wave functions. J. Electromagn. Waves Appl. 12 (6), pp. 709–711.

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ISSN 0920-5071, Document, MathReview

Referenced by:

§30.14(v).

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Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Differential Equations 162 (1), pp. 27–63.

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ISSN 0022-0396, Document, MathReview (John Albert), ZentralBlatt

Referenced by:

§22.19(iii).

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Deep water ship-waves. Phil. Mag. 9, pp. 733–757.

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External Links:

ZentralBlatt

Referenced by:

§36.13.

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15: Bibliography I

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Theta Functions. Springer-Verlag, New York.

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Notes:

Die Grundlehren der mathematischen Wissenschaften, Band 194

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ISBN 3540056998, MathReview (H. Klingen), ZentralBlatt

Referenced by:

§21.5(ii), §21.8, Ch.21.

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The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.

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ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§3.8(iii).

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Tables of the elliptic cylinder functions. Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.

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ZentralBlatt

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4th item, 2nd item.

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The periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 47–63.

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External Links:

MathReview (H. Bateman), ZentralBlatt

Referenced by:

§29.1, §29.15(ii), 1st item, §29.7(i).

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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).

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16: Bibliography C

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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

Referenced by:

§13.29(v), §15.19(v).

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Product formulas and convolutions for angular and radial spheroidal wave functions. Trans. Amer. Math. Soc. 338 (2), pp. 695–710.

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ISSN 0002-9947, FullText, MathReview (Jean-Claude Lucquiaud), ZentralBlatt

Referenced by:

§30.10, §30.11(vi).

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Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

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Document

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5th item.

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Coulomb Wave Functions. Roy. Soc. Math. Tables, Vol. 11, Cambridge University Press, Cambridge.

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ISBN 0-521-06156-3, MathReview (John Todd), ZentralBlatt

Referenced by:

item Curtis (1964a):, §33.14(i), §33.20(iv), §33.21(ii), §33.23(vi), 2nd item, §33.9(ii), Notations P, Notations Q.

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17: Bibliography R

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Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.

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Document

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6th item.

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Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.

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External Links:

MathReview (H. H. Martens), ZentralBlatt

Referenced by:

§20.11(iv), §20.12(ii).

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.

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MathReview (J. Shmoys)

Referenced by:

§12.17.

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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.

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External Links:

ISBN 3-7643-6287-1, MathReview Entry, ZentralBlatt

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5th item.

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18: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

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

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Online edition, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§11.12.

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Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.

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External Links:

Document, ZentralBlatt

Referenced by:

§33.5(ii).

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Linear and Nonlinear Waves. John Wiley & Sons, New York.

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Notes:

Reprinted in 1999.

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ISBN 0471359424, MathReview, ZentralBlatt

Referenced by:

§9.16.

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A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.

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Document, MathReview (T. B. Benjamin), ZentralBlatt

Referenced by:

§21.9.

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19: Bibliography D

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The KP equation with quasiperiodic initial data. Phys. D 123 (1-4), pp. 123–152.

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Notes:

Nonlinear waves and solitons in physical systems (Los Alamos, NM, 1997)

External Links:

ISSN 0167-2789, Document, MathReview (Pavel Krejčí), ZentralBlatt

Referenced by:

§21.9.

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Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.

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External Links:

Document

Referenced by:

§15.18.

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Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

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Notes:

For a numerical error in one of the zeros see Amos (1985).

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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2nd item.

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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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Coulomb wave functions with complex values of the variable and the parameters. J. Math. Phys. 40 (12), pp. 6145–6166.

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External Links:

ISSN 0022-2488, Document, MathReview (Raj Wilson), ZentralBlatt

Referenced by:

§33.13.

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