cylindrical coordinates

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1: 1.5 Calculus of Two or More Variables

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Cylindrical Coordinates

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1.5.15 $${\nabla }^{2}f=\frac{{\partial }^{2}f}{{\partial x}^2}+\frac{{\partial }^{2}f}{{\partial y}^2}+\frac{{\partial }^{2}f}{{\partial z}^2}=\frac{{\partial }^{2}f}{{\partial r}^2}+\frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^2}\frac{{\partial }^{2}f}{{\partial \varphi }^2}+\frac{{\partial }^{2}f}{{\partial z}^2}.$$

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Symbols:

$\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $z$: variable, $\varphi$: longitude and $r$: radius

Permalink:

http://dlmf.nist.gov/1.5.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §1.5(ii), §1.5(ii), §1.5 and Ch.1

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2: 10.73 Physical Applications

… ►In cylindrical coordinates $r$, $\varphi$, $z$, (§1.5(ii) we have … ►On separation of variables into cylindrical coordinates, the Bessel functions $J_n\left(x\right)$, and modified Bessel functions $I_n\left(x\right)$ and $K_n\left(x\right)$, all appear. …

3: 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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Calculation of zeros of cylindrical functions and their derivatives. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (2), pp. 63–64, 71 (Russian).

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Notes:

In Russian

External Links:

ISSN 0137-0782, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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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4: Bibliography H

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Certain sums that contain cylindrical functions. Bul. Akad. Štiince RSS Moldoven. 1972 (3), pp. 75–77, 94 (Russian).

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External Links:

MathReview (D. P. Gupta)

Referenced by:

§7.14(iii).

Encodings:

BibTeX

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Sums with cylindrical functions that reduce to the probability function and to related functions. Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).

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External Links:

MathReview (M. Lawrence Glasser)

Referenced by:

§7.14(iii).

Encodings:

BibTeX

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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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