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11: 30.14 Wave Equation in Oblate Spheroidal Coordinates

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§30.14(i) Oblate Spheroidal Coordinates

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12: 14.19 Toroidal (or Ring) Functions

… ►This form of the differential equation arises when Laplace’s equation is transformed into toroidal coordinates $(\eta ,\theta ,\varphi )$, which are related to Cartesian coordinates $(x,y,z)$ by …

13: 23.20 Mathematical Applications

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23.20.2 $$C:y^{2}z=x^3+ax{z}^2+b{z}^3,$$

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Symbols:

$x$: real part of $z$ , $y$: imaginary part of $z$ , $z$: complex, $C$: elliptic curve, $a$: constant and $b$: constant

Permalink:

http://dlmf.nist.gov/23.20.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §23.20(ii), §23.20 and Ch.23

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14: 30.13 Wave Equation in Prolate Spheroidal Coordinates

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§30.13(i) Prolate Spheroidal Coordinates

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15: Bibliography P

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Comoving coordinate system for relativistic hydrodynamics. Phy. Rev. C 75, pp. (024907–1)–(024907–10).

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External Links:

Document

Referenced by:

§7.21.

Encodings:

BibTeX

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16: 18.39 Applications in the Physical Sciences

… ►By (1.5.17) the first term in (18.39.21), which is the quantum kinetic energy operator $T_e$, can be written in spherical coordinates $r,\theta ,\varphi$ as …

17: Bibliography M

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Field Theory Handbook. Including Coordinate Systems, Differential Equations and Their Solutions. 2nd edition, Springer-Verlag, Berlin.

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Notes:

Reprinted in 1988.

External Links:

ISBN 3-540-18430-9, MathReview

Referenced by:

Table 28.1.1.

Encodings:

BibTeX

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18: 32.6 Hamiltonian Structure

… ► ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ can be written as a Hamiltonian system …

19: Guide to Searching the DLMF

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Table 2: Wildcard Examples

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Query	What it stands for
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co$te	Coordinate, conjugate, correlate,…
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… ►If a query does not return any hits, the DLMF search system relaxes the query to match and retrieve what may be intended by the original query. …Therefore, if your query is Ai^2+Bi^2, the system modifies the query so it will find the equations containing the latter expressions. … ►To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form. … ►The syntax of the special functions can be LaTeX-like or as employed in widely used computer algebra systems. …

20: 28.33 Physical Applications

… ►Physical problems involving Mathieu functions include vibrational problems in elliptical coordinates; see (28.32.1). …In elliptical coordinates (28.32.2) becomes (28.32.3). … ►

Daymond (1955) for vibrating systems.

… ►If the parameters of a physical system vary periodically with time, then the question of stability arises, for example, a mathematical pendulum whose length varies as $\cos \left(2\omega t\right)$. … ►

McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.

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