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The method
m: 0 1 2 3
Many orthogonal bases exist
0
1
In example:
Spherical harmonics,
, are a
) ,(
m
lY
l:
2
3
series of functions defined on the surface
of a sphere that exhibit orthogonality:
'
m m
δ δ d
1
)
( ) ('
) (
dφ dθ sin
2
) ,( ' ) ,(
d
mY mY
lY
lY
and therefore they can be used to expand
ll'
mm'
φ
2 1
cos
,
'
,
l
l
any function defined on the surface of a
sphere in an infinite series:
l
Various types of spherical harmonics
are available.
A particular set, of order l=N
d mY f
C
l
m
lY
l m
mlC
f
) (
) (
,
0
) ,(
,
) ,(
(orthogonal
basis)
+ the
corresponding weights of a function
are called a
quadrature set of
l
ml
,
,
,
order N
.