Spherical Harmonics Yl / Multipole |
Symmetric Power [Γl(xyz)] |
l |
2l+1 |
Multipole |
Symmetry |
Rank |
[Γl(xyz)] |
s (l=0) |
1 |
Monopole |
A' |
1 |
A' |
p (l=1) |
3 |
Dipole |
E'1⊕A'' |
3 |
E'1⊕A'' |
d (l=2) |
5 |
Quadrupole |
A'⊕E'2⊕E''1 |
6 |
2A'⊕E'2⊕E''1 |
f (l=3) |
7 |
Octupole |
E'1⊕E'3⊕A''⊕E''2 |
10 |
2E'1⊕E'3⊕2A''⊕E''2 |
g (l=4) |
9 |
Hexadecapole |
A'⊕E'2⊕E'4⊕E''1⊕E''3 |
15 |
3A'⊕2E'2⊕E'4⊕2E''1⊕E''3 |
h (l=5) |
11 |
Dotricontapole |
E'1⊕E'3⊕E'4⊕A''⊕E''2⊕E''4 |
21 |
3E'1⊕2E'3⊕E'4⊕3A''⊕2E''2⊕E''4 |
i (l=6) |
13 |
Tetrahexacontapole |
A'⊕E'2⊕E'3⊕E'4⊕E''1⊕E''3⊕E''4 |
28 |
4A'⊕3E'2⊕E'3⊕2E'4⊕3E''1⊕2E''3⊕E''4 |
j (l=7) |
15 |
Octacosahectapole |
E'1⊕E'2⊕E'3⊕E'4⊕A''⊕E''2⊕E''3⊕E''4 |
36 |
4E'1⊕E'2⊕3E'3⊕2E'4⊕4A''⊕3E''2⊕E''3⊕2E''4 |
k (l=8) |
17 |
256-pole |
A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E''1⊕E''2⊕E''3⊕E''4 |
45 |
5A'⊕E'1⊕4E'2⊕2E'3⊕3E'4⊕4E''1⊕E''2⊕3E''3⊕2E''4 |
l (l=9) |
19 |
512-pole |
2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕A''⊕E''1⊕E''2⊕E''3⊕E''4 |
55 |
2A'⊕5E'1⊕2E'2⊕4E'3⊕3E'4⊕5A''⊕E''1⊕4E''2⊕2E''3⊕3E''4 |
m (l=10) |
21 |
1024-pole |
A'⊕2E'1⊕E'2⊕E'3⊕E'4⊕2A''⊕E''1⊕E''2⊕E''3⊕E''4 |
66 |
6A'⊕3E'1⊕5E'2⊕3E'3⊕4E'4⊕2A''⊕5E''1⊕2E''2⊕4E''3⊕3E''4 |
n (l=11) |
23 |
2048-pole |
2A'⊕E'1⊕2E'2⊕E'3⊕E'4⊕A''⊕2E''1⊕E''2⊕E''3⊕E''4 |
78 |
4A'⊕6E'1⊕4E'2⊕5E'3⊕4E'4⊕6A''⊕3E''1⊕5E''2⊕3E''3⊕4E''4 |
o (l=12) |
25 |
4096-pole |
A'⊕2E'1⊕E'2⊕2E'3⊕E'4⊕2A''⊕E''1⊕2E''2⊕E''3⊕E''4 |
91 |
7A'⊕5E'1⊕6E'2⊕5E'3⊕5E'4⊕4A''⊕6E''1⊕4E''2⊕5E''3⊕4E''4 |
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