spheroidal coordinates

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1: 30.14 Wave Equation in Oblate Spheroidal Coordinates

§30.14 Wave Equation in Oblate Spheroidal Coordinates

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§30.14(i) Oblate Spheroidal Coordinates

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§30.14(ii) Metric Coefficients

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§30.14(iii) Laplacian

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2: 30.13 Wave Equation in Prolate Spheroidal Coordinates

§30.13 Wave Equation in Prolate Spheroidal Coordinates

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§30.13(i) Prolate Spheroidal Coordinates

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§30.13(ii) Metric Coefficients

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§30.13(iii) Laplacian

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3: 30.1 Special Notation

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4: 30.2 Differential Equations

… ►In applications involving prolate spheroidal coordinates ${\gamma }^2$ is positive, in applications involving oblate spheroidal coordinates ${\gamma }^2$ is negative; see §§30.13, 30.14. …

5: 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.

Encodings:

BibTeX

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Tables of Radial Spheroidal Wave Functions, Vols. 1-3, Prolate, $m=0,1,2$; Vols. 4-6, Oblate, $m=0,1,2$ . Technical report Naval Research Laboratory, Washington, D.C..

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Notes:

NRL Reports 7088-7093

External Links:

ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

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The eigenvalues of the angular spheroidal wave equation. Stud. Appl. Math. 66 (3), pp. 217–240.

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External Links:

ISSN 0022-2526, MathReview, ZentralBlatt

Referenced by:

§30.9(iii).

Encodings:

BibTeX

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6: 31.17 Physical Applications

… ►Introduce elliptic coordinates $z_1$ and $z_2$ on $S_2$. Then ►

31.17.2 $$\frac{x_s^2}{z_k}+\frac{x_t^2}{z_k-1}+\frac{x_u^2}{z_k-a}=0,$$ $k=1,2$,

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Symbols:

$z$: complex variable, $a$: complex parameter and $x_s$, $x_t$, $x_u$: coordinates

Permalink:

http://dlmf.nist.gov/31.17.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §31.17(i), §31.17 and Ch.31

… ►More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver (1986) and Slavyanov and Lay (2000, Chapter 4). …

7: Bibliography M

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Catastrophe optics of spheroidal drops and generalized rainbows. J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.

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External Links:

Document

Referenced by:

§36.14(ii).

Encodings:

BibTeX

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Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.

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External Links:

MathReview (M. L. Mehta), ZentralBlatt

Referenced by:

§30.9(i).

Encodings:

BibTeX

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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:

BibTeX

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Spheroidal eigenfunctions of the tidal equation. Phys. Rev. Lett. 73 (11), pp. 1557–1560.

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External Links:

ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

BibTeX

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