sphero-conal coordinates

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31: 22.18 Mathematical Applications

… ►In polar coordinates, $x=r\cos \varphi$, $y=r\sin \varphi$, the lemniscate is given by $r^2=\cos \left(2\varphi \right)$, $0\le \varphi \le 2\pi$. …

32: 36.7 Zeros

… ►There are also three sets of zero lines in the plane $z=0$ related by $2\pi /3$ rotation; these are zeros of (36.2.20), whose asymptotic form in polar coordinates $(x=r\cos \theta ,y=r\sin \theta )$ is given by …

33: 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.

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34: Bibliography R

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Complex Coordinates in the Theory of Atomic and Molecular Structure and Dynamics. Annual Review of Physical Chemistry 33, pp. 223–255.

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Referenced by:

§1.18(viii).

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35: Bibliography H

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The combination of $R$-matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.

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External Links:

ISSN 0953-4075, Document, MathReview

Referenced by:

4th item.

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36: Bibliography M

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Lie theory and separation of variables. I: Parabolic cylinder coordinates. SIAM J. Math. Anal. 5 (4), pp. 626–643.

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External Links:

Document, MathReview (G. R. Allcock), ZentralBlatt

Referenced by:

§12.13(ii), §12.17.

Encodings:

BibTeX

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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:

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37: 33.22 Particle Scattering and Atomic and Molecular Spectra

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Eigenstates using complex-rotated coordinates $r\to r{\mathrm{e}}^{\mathrm{i}\theta }$, so that resonances have square-integrable eigenfunctions. See for example Halley et al. (1993).

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38: 31.10 Integral Equations and Representations

… ►A further change of variables, to spherical coordinates, …

39: 1.15 Summability Methods

… ► $A(r,\theta )$ is a harmonic function in polar coordinates (1.9.27), and …

40: 3.5 Quadrature

… ►The steepest descent path is given by $\mathrm{\Im }\left(t-2\sqrt{t}\right)=0$, or in polar coordinates $t=r{\mathrm{e}}^{\mathrm{i}\theta }$ we have $r={\sec }^2\left(\frac{1}{2}\theta \right)$. …