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1: 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

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§29.19(ii).

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Linear Turning Point Theory. Applied Mathematical Sciences No. 54, Springer-Verlag, New York.

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ISBN 0-387-96046-5, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

Ch.9.

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Hill’s equation with a large potential. SIAM J. Appl. Math. 45 (2), pp. 200–214.

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ISSN 0036-1399, Document, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§29.7(ii).

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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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Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (4), pp. 525–536.

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ISSN 0010-3616, Document, MathReview (J. Stasheff), ZentralBlatt

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1st item.

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2: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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Document

Referenced by:

§33.22(iv).

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The attractive Coulomb potential polynomials. Constr. Approx. 1 (2), pp. 103–119.

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ISSN 0176-4276, Document, Link, MathReview (W. A. Al-Salam)

Referenced by:

§18.39(iv), §18.39(iv).

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Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.

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Document, ZentralBlatt

Referenced by:

§36.14(iii), §9.16.

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A class of solvable potentials. Nuovo Cimento (10) 25, pp. 864–879.

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Document, MathReview (S. Rosendorff), ZentralBlatt

Referenced by:

§15.18.

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Stability of repulsive Bose-Einstein condensates in a periodic potential. Phys. Rev. E (3) 63 (036612), pp. 1–11.

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Document

Referenced by:

§29.19(i).

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3: Bibliography N

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Confluent hypergeometric equations and related solvable potentials in quantum mechanics. J. Math. Phys. 41 (12), pp. 7964–7996.

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ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§13.28(i).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

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Handbuch der Theorie der Gammafunktion. B. G. Teubner, Leipzig (German).

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Notes:

For a reprint with corrections see Nielsen (1965).

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ZentralBlatt (G. Kowalewski)

Referenced by:

§5.12, Ch.5, §6.10(i), §6.10(i), §7.9, §8.1.

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Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten. Chelsea Publishing Co., New York (German).

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Notes:

Both books are textually unaltered except for correction of errata.

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MathReview

Referenced by:

N. Nielsen (1906a), N. Nielsen (1906b).

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Notes:

References and links to software for factorization and primality testing.

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Home Page

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6th item.

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4: 10.73 Physical Applications

… ►Laplace’s equation governs problems in heat conduction, in the distribution of potential in an electrostatic field, and in hydrodynamics in the irrotational motion of an incompressible fluid. … ►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25). … ►In the theory of plates and shells, the oscillations of a circular plate are determined by the differential equation … ►In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential. …

5: 18.39 Applications in the Physical Sciences

… ►defines the potential for a symmetric restoring force $-kx$ for displacements from $x=0$. … ►argument b) The Morse Oscillator … ►c) A Rational SUSY Potential argument ►The Schrödinger equation with potential … ►Now use spherical coordinates (1.5.16) with $r$ instead of $\rho$, and assume the potential $V$ to be radial. …

6: Bibliography G

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WKB and turning point theory for second-order difference equations. In Spectral Methods for Operators of Mathematical Physics, Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.

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FullText, MathReview (Ioannis K. Purnaras), ZentralBlatt

Referenced by:

§18.15(v), §18.15(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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Constructing wavefunctions for nonlocal potentials. J. Chem. Phys. 52, pp. 6211–6217.

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Document, MathReview (D. B. Fairlie)

Referenced by:

(9.12.22), (9.12.23), §9.12(vii), §9.17(iii).

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Linear Differential Equations and Group Theory from Riemann to Poincaré. 2nd edition, Birkhäuser Boston Inc., Boston, MA.

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ISBN 0-8176-3837-7, MathReview, ZentralBlatt

Referenced by:

§15.17(v).

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Kinetic theory of linear shear flow. Phys. Fluids 1 (3), pp. 215–224.

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Referenced by:

§18.39(iii).

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7: Bibliography

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Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

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MathReview, ZentralBlatt

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1st item.

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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

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Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

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Document, ZentralBlatt

Referenced by:

§11.12.

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Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions. J. Mathematical Phys. 16, pp. 961–970.

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Notes:

Erratum: same journal 17 (1975), no. 7, p. 1361

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Document, MathReview (K. Veselic), ZentralBlatt

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4th item.

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Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.

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Referenced by:

§27.13(i), §27.15, §27.16, Ch.27.

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8: Bibliography D

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Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.

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Notes:

Revised and with a preface by Hugh L. Montgomery

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ISBN 0-387-95097-4, MathReview, ZentralBlatt

Referenced by:

§27.12.

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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction $\zeta (s)$ de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann. Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).

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Notes:

Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 223–296 Académie Royale de Belgique, Brussels, 2000.

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MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire $Mx+N$ . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).

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Notes:

Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 309–425, Académie Royale de Belgique, Brussels, 2000.

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MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

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

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Document

Referenced by:

§15.18.

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Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.

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Referenced by:

§18.38(iii).

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9: Bibliography M

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The Theory of Groups. Clarendon Press, Oxford.

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Notes:

Reprinted in 1988 by Krieger Publishing Co., Malabar, FL

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ISBN 0-19-853137-0;0-89464-287-1, MathReview (A. P. Street), ZentralBlatt

Referenced by:

§23.20(ii).

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Zur Theorie des zylindrisch-parabolischen Spiegels. Z. Physik 118, pp. 343–356 (German).

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MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§12.17.

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Loud Speakers: Theory, Performance, Testing and Design. Oxford University Press, New York.

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Notes:

Reprinted, with corrections, by Dover Publications Inc., 1960.

External Links:

MathReview, ZentralBlatt

Referenced by:

§11.12.

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Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions. Comput. Phys. Comm. 178 (7), pp. 535–551.

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ISSN 0010-4655, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§15.19(i), §15.19(i).

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The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

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ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

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10: Bibliography S

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Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

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External Links:

Document

Referenced by:

§33.14(i), §33.22(ii).

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Coulomb functions for attractive and repulsive potentials and for positive and negative energies. Comput. Phys. Comm. 146 (2), pp. 225–249.

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External Links:

ISSN 0010-4655, Document, MathReview, ZentralBlatt

Referenced by:

§1.17(ii), §33.1, §33.14(i), §33.14(ii), §33.14(iii), §33.14(iv), §33.14(v), §33.16(i), §33.16(ii), §33.16(iii), §33.16(v), §33.17, §33.19, §33.20(i), §33.20(ii), §33.20(iii), §33.21(i), Ch.33.

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Resonances in $n$-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Ann. of Math. (2) 97, pp. 247–274.

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ISSN 0003-486X, Document, Link, MathReview (K. Kumar)

Referenced by:

§1.18(viii).

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Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview (R. Shail), ZentralBlatt

Referenced by:

§10.22(iv).

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BibTeX

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Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. National Bureau of Standards Applied Mathematics Series, No. 19, U. S. Government Printing Office, Washington, D.C..

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.23(iv), Ch.14, §31.3(iii).

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