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

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

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

New in version 0.15.0.

Examples

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

scipy.special.ellip_harm_2 scipy.special.assoc_laguerre