©2005-2018 Ulm University, Othmar Marti, pict
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A.1  Zugeordnete Kugelfunktionen



= 0
m = 0
pict
P00(cos2𝜃) = 1


= 1
m = 0
pict
P10(cos2𝜃) = (cos(𝜃)) 2


= 1
m = 1
pict
P11    2
(cos 𝜃) = ∘ ------------4
  1 − (cos(𝜃))


= 2
m = 0
pict
P20(cos2𝜃) = 32(cos (𝜃)) 4 12


= 2
m = 1
pict
P21    2
(cos 𝜃) = 3∘ ------------4
  1 − (cos(𝜃))(cos (𝜃)) 2


= 2
m = 2
pict
P22(cos2𝜃) = 3 3(cos(𝜃)) 4


= 3
m = 0
pict
P30    2
(cos 𝜃) = (cos(𝜃)) 6 + 32(        4    )
 (cos(𝜃)) −  1(cos(𝜃)) 2


= 3
m = 1
pict
P31(cos2𝜃) = ∘ -------------
  1 − (cos(𝜃))4 (                    )
 15∕2 (cos(𝜃))4 − 3∕2


= 3
m = 2
pict
P32(cos2𝜃) = 15(             )
  1 − (cos (𝜃))4(cos (𝜃)) 2


= 3
m = 3
pict
P33(cos2𝜃) = 15(            4)
  1 − (cos (𝜃))32


= 4
m = 0
pict
P40(cos2𝜃) = (cos(𝜃)) 8 + 3(             )
 (cos(𝜃))4 − 1(cos (𝜃)) 4 + 38(             )
 (cos (𝜃))4 − 12


= 5
m = 0
pict
P50(cos2𝜃) = (cos(𝜃)) 10 + 5(            )
 (cos(𝜃))4 − 1(cos (𝜃 )) 6 + 15-
8(             )
 (cos(𝜃))4 − 12(cos (𝜃)) 2


Zugeordnete Kugelfunktionen



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