sphero-conal

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1: 29.18 Mathematical Applications

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§29.18(i) Sphero-Conal Coordinates

… ►when transformed to sphero-conal coordinates $r,\beta ,\gamma$: … ►

29.18.4 $$u(r,\beta ,\gamma )=u_1(r)u_2(\beta )u_3(\gamma ),$$

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Symbols:

$u$: solution, $r$: sphero-conal coordinate, $\beta$: sphero-conal coordinate, $\gamma$: sphero-conal coordinate and $u_j$: solutions

Permalink:

http://dlmf.nist.gov/29.18.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §29.18(i), §29.18 and Ch.29

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29.18.5 $$\frac{d}{dr}\left(r^2\frac{d{u}_1}{dr}\right)+({\omega }^2{r}^2-\nu (\nu +1))u_1=0,$$

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Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $\nu$: real parameter, $\omega$: parameter, $r$: sphero-conal coordinate and $u_j$: solutions

Referenced by:

§29.18(i)

Permalink:

http://dlmf.nist.gov/29.18.E5

Encodings:

pMML, png, TeX

See also:

Annotations for §29.18(i), §29.18 and Ch.29

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29.18.6 $$\frac{d^2{u}_2}{{d\beta }^2}+(h-\nu (\nu +1)k^2{\mathrm{sn}}^2(\beta ,k))u_2=0,$$

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Symbols:

$\mathrm{sn}(z,k)$: Jacobian elliptic function, $\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $h$: real parameter, $k$: real parameter, $\nu$: real parameter, $\beta$: sphero-conal coordinate and $u_j$: solutions

Referenced by:

§29.18(i)

Permalink:

http://dlmf.nist.gov/29.18.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §29.18(i), §29.18 and Ch.29

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