II
=
883
INDUCTION IN ROTATING SPHERES
then
Let
Xn = A
-
\n+1
cos iwPni
If we write
K
Ap
n+¹i
- sin iwP,
n
ni.
=
K
Ap
n
***, sin
n
(f, sin iw+f, cos iw)Pri
the function induced by becomes
2
=
-
Ap
p(2) ***
(F, cos iw - F, sin iw)Pni
2
K
n
But here the connection between f and F is somewhat
different from what it was before, for we have
F(p)=
4π
2n+1
af (a)da +
"
The condition
4=40+4
leads to the same equations as before,
iw.
f₁ = 1+2F₁₂,
K
R
2n+1
a2n
-f (a)a
axda}.
fa
iw Fr
K
Using the same contractions as before we get
8
1
$1(0) = 1 +
2n+1
U
ap(a)da+on+¹a'
2n
Φ.(σ)
= -
1
2n+1
S
8
ap₁(a)da + o²n +¹α'