scipy.special.

ellip_normal#

scipy.special.ellip_normal(h2, k2, n, p)[source]#

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.

Array API Standard Support

ellip_normal has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

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