scipy.special.

ellip_normal

scipy.special.ellip_normal(h2, k2, n, p)

Ellipsoidal harmonic normalization constants \(\gamma^p_n\).

The normalization constant is defined as

\[\gamma^p_n=8\int_{0}^{h}dx\int_{h}^{k}dy \frac{(y^2-x^2)(E^p_n(y)E^p_n(x))^2}{\sqrt{(k^2-y^2)(y^2-h^2)(h^2-x^2)(k^2-x^2)}}\]

where \(E^p_n\) are the ellipsoidal harmonic functions, see ellip_harm.

Parameters:

h2float

h**2.

k2float

k**2; should be larger than h**2.

nint

Degree.

pint

Order, can range between \([1, 2n+1]\).

Returns:

gammafloat

The normalization constant \(\gamma^p_n\).

See also

ellip_harm, ellip_harm_2

Notes

Added in version 0.15.0.

Examples

Try it in your browser!

>>> from scipy.special import ellip_normal
>>> w = ellip_normal(5,8,3,7)
>>> w
1723.38796997

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