closed-form solutions

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1: 1.13 Differential Equations

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§1.13(vii) Closed-Form Solutions

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2: 20.13 Physical Applications

… ►This allows analytic time propagation of quantum wave-packets in a box, or on a ring, as closed-form solutions of the time-dependent Schrödinger equation.

3: Bibliography O

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A closed form solution of the $s$-wave Bethe-Goldstone equation with an infinite repulsive core. J. Math. Phys. 27 (4), pp. 1154–1158.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

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4: 32.2 Differential Equations

… ►For arbitrary values of the parameters $\alpha$, $\beta$, $\gamma$, and $\delta$, the general solutions of ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ are transcendental, that is, they cannot be expressed in closed-form elementary functions. …

5: Bibliography K

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Determinant structure of the rational solutions for the Painlevé II equation. J. Math. Phys. 37 (9), pp. 4693–4704.

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ISSN 0022-2488, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.8(ii).

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Closed-form representations of the Lambert $W$ function. Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.

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ISSN 1311-0454, MathReview (Lewis H. Ryder), ZentralBlatt

Referenced by:

§4.13.

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

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ISSN 0022-1120, Document, MathReview, ZentralBlatt

Referenced by:

§19.35(ii).

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Introduction to Elliptic Curves and Modular Forms. 2nd edition, Graduate Texts in Mathematics, Vol. 97, Springer-Verlag, New York.

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External Links:

ISBN 0-387-97966-2, MathReview, ZentralBlatt

Referenced by:

§20.10(i), §20.12(i), §20.9(iii), §22.18(iv), §23.1, §23.20(ii), §23.20(v), Ch.23.

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Asymptotic solution of Maxwell’s equations near caustics. Izv. Vuz. Radiofiz. 7, pp. 1049–1056.

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Referenced by:

§36.14(i).

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6: Bibliography C

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Analytical solution of a model for complex food webs. Phys. Rev. E 65 (3), pp. (030901–1)–(030901–4).

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Document

Referenced by:

§8.24(i).

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Intégrandes à deux formes quadratiques. C. R. Acad. Sci. Paris Sér. A–B 274 (15 May, 1972, Sér. A), pp. 1458–1461 (French).

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External Links:

MathReview (J. A. Donaldson), ZentralBlatt

Referenced by:

§19.31.

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Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity. Phys. Rev. A 62 (063610), pp. 1–10.

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Document

Referenced by:

§22.19(iii).

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Asymptotics and closed form of a generalized incomplete gamma function. J. Comput. Appl. Math. 67 (2), pp. 371–379.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.16.

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Modular Forms and Fermat’s Last Theorem. Springer-Verlag, New York.

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External Links:

ISBN 0-387-94609-8; 0-387-98998-6, MathReview (M. Ram Murty), ZentralBlatt

Referenced by:

§23.20(v).

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