Spherical Harmonic Normalization Factors


We normalize spherical harmonic coefficients following Kaula [1966]*.

The formula is:
Factor(l,m) = sqrt[(l-m)!(2l+1)(2-Kron.del)/(l+m)!]
where
Kron.del = 1 for m = 0, 0 for m not= 0

Degree
Order
Normalization Factor
0
0
1
1
0
sqrt(3)
1
1
sqrt(3)
2
0
sqrt(5)
2
1
sqrt(5/3)
2
2
(1/2)sqrt(5/3)
3
0
sqrt(7)
3
1
sqrt(7/6)
3
2
(1/2)sqrt(7/15)
3
3
(1/6)sqrt(7/10)
4
0
sqrt(9)
4
1
sqrt(9/10)
and so on...

*Kaula, W.M., Theory of Satellite Geodesy,Blaisdell, 124 pp., Waltham, 1966.


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