Методы математической физики - 181 стр.

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a
k+1
=
k λ
(k + 1) (k + 1 + s)
a
k
.
e
x
λ =
n n n
L
s
n
(x)
Ψ(t, x) =
X
n=0
L
s
n
(x) t
n
=
1
(1 t)
s+1
e
xt/(1t)
.
L
s
n
(x) =
1
n!
x
s
e
x
d
n
dx
n
¡
x
n+s
e
x
¢
, n = 0 , 1 , 2 . . . .
n
L
s
0
(x) = 1 , L
s
1
(x) = x + 1 + s ,
L
s
2
(x) =
x
2
2
(2 + s) x +
(2 + s)(1 + s)
2
, . . .
[L
s
n+1
(x)]
0
= [L
s
n
(x)]
0
L
s
n
(x) ,
(n + 1) L
s
n+1
(x) (2n + 1 + s x) L
s
n
(x) + (n + s) L
s
n1
(x) = 0 .