`scipy.special._ellip_harm:ellip_normal`

Signature

def ellip_normal(h2, k2, n, p)

Ellipsoidal harmonic normalization constants $γ_{n}^{p}$ .

The normalization constant is defined as

γ_{n}^{p} = 8 \int_{0}^{h} d x \int_{h}^{k} d y \frac{( y ^{2} - x ^{2} ) ( E _{n}^{p} ( y ) E _{n}^{p} ( x ) ) ^{2}}{( k ^{2} - y ^{2} ) ( y ^{2} - h ^{2} ) ( h ^{2} - x ^{2} ) ( k ^{2} - x ^{2} )}

where $E_{n}^{p}$ are the ellipsoidal harmonic functions, see ellip_harm.

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

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array(1723.388)