Методы математической физики - 145 стр.

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ln(x/2) x
ν ν =
n
y
n
(x) = C
1
J
n
(x) + C
2
N
n
(x) .
H
(1)
ν
(x) J
ν
(x) + i N
ν
(x) ,
H
(2)
ν
(x) J
ν
(x) i N
ν
(x) ,
H
(1)
ν
(x) H
(2)
ν
(x)
ν
ν
H
(1)
ν
(x) =
J
ν
(x) J
ν
(x) e
iνπ
i sin νπ
,
H
(2)
ν
(x) =
J
ν
(x) J
ν
(x) e
iνπ
i sin νπ
.
y
00
+
1
x
y
0
µ
1 +
ν
2
x
2
y = 0 .
x
x ix x
y(x) = J
ν
(ix)