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A.1  Zugeordnete Kugelfunktionen



= 0
m = 0
PIC
P00(cos2θ) = 1


= 1
m = 0
PIC
P10(cos2θ) = (cos(θ)) 2


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


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


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


= 2
m = 2
PIC
P22(cos2θ) = 3 - 3(cos(θ)) 4


= 3
m = 0
PIC
P30    2
(cos θ) = (cos(θ)) 6 + 32(        4    )
 (cos(θ)) -  1(cos(θ)) 2


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


= 3
m = 2
PIC
P32(cos2θ) = 15(             )
  1 - (cos (θ))4(cos (θ)) 2


= 3
m = 3
PIC
P33(cos2θ) = 15(            4)
  1 - (cos (θ))32


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


= 5
m = 0
PIC
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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