©2005-2012 Ulm University, Othmar Marti
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A.1  Zugeordnete Kugelfunktionen

ℓ = 0
m = 0
PIC
P00(cos θ) = 1
ℓ = 1
m = 0
PIC
P10(cos θ) = (cos(θ)) 2
ℓ = 1
m = 1
PIC
P11(cos θ) = ∘ ------------- 1 - (cos(θ))4
ℓ = 2
m = 0
PIC
P20(cos θ) = 3∕2(cos (θ )) 4 - 1∕2
ℓ = 2
m = 1
PIC
P21(cos θ) = 3∘ ------------- 1 - (cos(θ))4(cos(θ)) 2
ℓ = 2
m = 2
PIC
P22(cos θ) = 3 - 3(cos(θ)) 4
ℓ = 3
m = 0
PIC
P30(cos θ) = (cos(θ)) 6 + 3∕2( 4 ) (cos(θ)) - 1(cos (θ)) 2
ℓ = 3
m = 1
PIC
P31(cos θ) = ∘ ------------- 1 - (cos(θ))4 ( ) 15∕2 (cos(θ))4 - 3 ∕2
ℓ = 3
m = 2
PIC
P32(cos θ) = 15( 4) 1 - (cos(θ))(cos(θ)) 2
ℓ = 3
m = 3
PIC
P33(cos θ) = 15( 4) 1 - (cos(θ))3∕2
ℓ = 4
m = 0
PIC
P40(cos θ) = (cos(θ)) 8 + 3( 4 ) (cos (θ)) - 1(cos(θ)) 4 + 3∕8( 4 ) (cos(θ)) - 12
ℓ = 5
m = 0
PIC
P50(cos θ) = (cos(θ)) 10 + 5( 4 ) (cos (θ )) - 1(cos(θ)) 6 + 15 -8( 4 ) (cos(θ)) - 12(cos(θ)) 2

Zugeordnete Kugelfunktionen


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