oscillations of chains

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11: Bibliography

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Nonlinear chains and Painlevé equations. Phys. D 73 (4), pp. 335–351.

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External Links:

ISSN 0167-2789, Document, MathReview (F. Pempinelli), ZentralBlatt

Referenced by:

§32.2(v).

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Umbral calculus, Bailey chains, and pentagonal number theorems. J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.

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Notes:

In memory of Gian-Carlo Rota

External Links:

ISSN 0097-3165, Document, MathReview (Alessandro Di Bucchianico), ZentralBlatt

Referenced by:

§17.12.

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Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.

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External Links:

ISBN 0-7923-7119-4, MathReview, ZentralBlatt

Referenced by:

§17.12.

Encodings:

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12: 1.4 Calculus of One Variable

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Chain Rule

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13: 1.5 Calculus of Two or More Variables

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Chain Rule

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14: 12.17 Physical Applications

… ►Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator. …

15: 36.13 Kelvin’s Ship-Wave Pattern

… ►When $\rho >1$, that is, everywhere except close to the ship, the integrand oscillates rapidly. …

16: Bibliography M

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New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..

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External Links:

MathReview Entry

Referenced by:

§18.36(vi).

Encodings:

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Connection between quantum systems involving the fourth Painlevé transcendent and $k$-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial. J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..

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External Links:

ISSN 0022-2488, Document, Link, MathReview Entry

Referenced by:

§18.38(iii).

Encodings:

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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems. Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.

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External Links:

FullText

Referenced by:

§8.24(i).

Encodings:

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Applying $q$-Laguerre polynomials to the derivation of $q$-deformed energies of oscillator and Coulomb systems. Romanian Reports in Physics 57 (1), pp. 25–34.

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Referenced by:

§17.17.

Encodings:

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17: Bibliography N

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Eigenstates, coherent states, and uncertainty products for the Morse oscillator. Phys. Rev. A (3) 19 (2), pp. 438–444.

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External Links:

ISSN 1050-2947, Document, Link, MathReview Entry

Referenced by:

(18.39.17), (18.39.18).

Encodings:

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18: 32.2 Differential Equations

… ►When $\beta =0$ this is a nonlinear harmonic oscillator. …

19: 28.33 Physical Applications

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Jager (1997, 1998) for relativistic oscillators.

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20: 18.36 Miscellaneous Polynomials

… ►In §18.39(i) it is seen that the functions, $\sqrt{w(x)}{\widehat{H}}_{n+3}\left(x\right)$, are solutions of a Schrödinger equation with a rational potential energy; and, in spite of first appearances, the Sturm oscillation theorem, Simon (2005c, Theorem 3.3, p. 35), is satisfied. …