Численные методы. Ч.1. Исследование функций. Буслов В.А - 26 стр.

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СПбГУ | Санкт-Петербург

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g = f
−1
f(0) 6= 0 [M/L]
g
= [L/M]
f
[L/M]
f
[L/M]
f
(z) =
P
L
(z)
Q
M
(z)
P
L
(0) 6= 0 [L/M]
f
(0) = f(0) 6= 0
g(z) −
Q
M
(z)
P
L
(z)
=
P
L
(z) − f(z)Q
M
(z)
f(z)P
L
(z)
= O(z
L+M+1
) ,
w =
az
1+bz
g(w) = f(z) [M/M]
g
(w) = [M/M ]
f
(z)
[M/M]
g
(w) =
M
P
a
k
w
k
M
P
b
k
w
k
= g(w) + O(z
2M+1
) .
A
M
B
M
z M
A(z) = (1 + bz)
M
M
X
a
k
µ
az
1 + bz
k
, B(z) = (1 + bz)
M
M
X
b
k
µ
az
1 + bz
k
,
A
M
(z)
B
M
(z)
= f(z) + O(z
2M+1
) ,
g(z) =
a+bf(z)
c+df(z)
c + df(0) 6= 0
[M/M]
g
(z) =
a + b[M/M]
f
c + d[M/M]
f
,
[M/M]
f
a + b[M/M]
f
(z)
c + d[M/M]
f
(z)
=
P
M
(z)
Q
M
(z)
,
P
M
Q
M
M Q
M
(0) 6= 0
P
M
(z)
Q
M
(z)
− g(z) =
(bc − ad) {[M/M]
f
(z) − f(z)}
{c + d[M/M]
f
(z)}(c + df(z))
= O(z
2M+1
) .
f(z) =
∞
X
k=0
f
k
z
k+1
z N
Q
N
6= 0 degQ
N
≤ N
Q
N
(z)f(z) −P
N
(z) =
c
z
N+1
+ . . . , (11)

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