Методы математической физики - 142 стр.

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λ λ
i
=
(µ
i
/ρ
0
)
2
J
ν
(x) x
ν
x
x
ν
d
dx
J
ν
(x)
x
ν
=
1
2
ν
∞
X
m=1
(−1)
m
m
Γ(m + 1)Γ(m + 1 + ν)
³
x
2
´
2m−1
¯
¯
¯
¯
¯
m−1=m
0
=
=
1
2
ν
∞
X
m
0
=0
(−1)
m
0
+1
Γ(m
0
+ 1)Γ(m
0
+ 2 + ν)
³
x
2
´
2m
0
+1
= −
J
ν+1
(x)
x
ν
.
1
x
d
dx
J
ν
(x)
x
ν
= −
J
ν+1
(x)
x
ν+1
.
x x
µ
1
x
d
dx
n
J
ν
(x)
x
ν
= (−1)
n
J
ν+n
(x)
x
ν+n
.
1
x
d
dx
[x
ν
J
ν
(x)] = x
ν−1
J
ν−1
(x) ,
µ
1
x
d
dx
n
[x
ν
J
ν
(x)] = x
ν−n
J
ν−n
(x) .
1
x
·
J
0
ν
(x)
x
ν
− ν
J
ν
(x)
x
ν+1
¸
= −
J
ν+1(x)
x
ν+1
,
J
0
ν
(x) = −J
ν+1
(x) + ν
J
ν
(x)
x
.

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