.
GNU_ScientificLibrary
.
Examples
.
specfunc
.
CoaxialDirichlet
Information
U
nm
(r,phi,z) = R
n
(kr) Z(kz) e
i*m*phi
.
R
n
(kr) = A
n
J
n
(kr) + B
n
Y
n
(kr) .
R
n
(x
ni
) = A
n
J
n
(x
ni
) + B
n
Y
n
(x
ni
) = 0 --> R
n
(x) = Y
n
(x
n0
) J
n
(x) - J
n
(x
n0
) Y
n
(x) ...
R
n
(x
nj
) = Y
n
(x
n0
) J
n
(x
nj
) - J
n
(x
n0
) Y
n
(x
nj
) = 0 .
x
nj
- x
n0
= k
j
(b - a) ; or rather, x
n0
(x
nj
/x
n0
- 1) = k
j
a (b/a - 1) .
So for each mode (n,j), x
n0
needs to be adjusted until x
nj
/x
n0
= b/a ; then k
j
= x
n0
/a = x
nj
/b .
R
n
(kr) = C
n
I
n
(kr) + D
n
K
n
(kr) .
R
n
(x
n0
) = C
n
I
n
(x
n0
) + D
n
K
n
(x
n0
) = 0 --> R
n
(x) = K
n
(x
n0
) I
n
(x) - I
n
(x
n0
) K
n
(x) .
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.GNU_ScientificLibrary.Examples.specfunc.CoaxialDirichlet .GNU_ScientificLibrary.Examples.specfunc.CoaxialDirichlet