Tabellenanhang - Alex-weingarten.de

84 ANHANG O. BEISPIELE LATEX
∀x, y, z ∈ M : (xRy ∧ xRz) ⇒ y = z (O.19)
A · B = Ā + ¯B
ρ · ¯v k · ∂¯v j
= − ∂ ¯p +
∂ (
µ ∂¯v )
j
− ρ v k ′ ∂x k ∂x j ∂x k ∂x v′ j
k
(O.20)
(O.21)
r ′ =
v 1v ′ 2
′ √ √ (O.22)
¯ ¯ v′2 1 v′2 2
τ tur = ρl 2 | ∂ ¯v 1
∂x 2
| ∂ ¯v 1
∂x 2
(O.23)
¨R = 1 Ψ (V 2
r − Ṙ) + R ˙Φ
¨Φ = [ 1 Ψ (V ϕ − R ˙Φ) − 2Ṙ ˙Φ] 1 R
(O.24)
¨Z = 1 Ψ (V Z − Ż)
ˆχ 2 =
n(n − 1)
B(n − B)
V (r, ϑ, ϕ) =
∞∑
l=0
k∑ (B i − E i ) 2
> χ 2 k−1;α (O.25)
i=1
n i
4π
2l + 1
l∑
m=−l
q l,m
Y l,m ϑ, ϕ)
r l+1
(O.26)
q ′ l ′ ,m ′ = ∞ ∑
o∑
o=0 p=−o
⃗q =
⎜
⎝
⎛ ⎞
q 0,0
q 1,1
q 1,0
q 1,−1
q 2,2
q 2,1
q 2,0
⎟
q 2,−1 ⎠
q 2,−2
n o,p q o,p (∇) l ′ +o,m ′ −p;o,p
q l,m = −q ′ l,mR 2l+1 l(ɛ i − ɛ a )
l(ɛ a + ɛ i ) + ɛ a
Y l ′ +o,m ′ −p(ϑ a , ϕ a )
a l′ +o+1
(O.27)
(O.28)
(O.29)
⃗q ′ 1,1 = ⃗q ′ 1,0 + I 2,1
⃗q ′ 2,0
⃗q ′ 2,1 = ⃗q ′ 2,0 + I 1,2
⃗q ′ 1,0
(O.30)
(O.31)