closed-form solutions
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6 matching pages
1: 1.13 Differential Equations
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§1.13(vii) Closed-Form Solutions
…2: 20.13 Physical Applications
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►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 -wave Bethe-Goldstone equation with an infinite repulsive core.
J. Math. Phys. 27 (4), pp. 1154–1158.
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4: 32.2 Differential Equations
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►For arbitrary values of the parameters , , , and , the general solutions of – are transcendental, that is, they cannot be expressed in closed-form elementary functions.
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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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Closed-form representations of the Lambert function.
Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
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A vortex filament moving without change of form.
J. Fluid Mech. 112, pp. 397–409.
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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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Asymptotic solution of Maxwell’s equations near caustics.
Izv. Vuz. Radiofiz. 7, pp. 1049–1056.
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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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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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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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Asymptotics and closed form of a generalized incomplete gamma function.
J. Comput. Appl. Math. 67 (2), pp. 371–379.
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Modular Forms and Fermat’s Last Theorem.
Springer-Verlag, New York.
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