,
, .
2.1.1. y ( n ) = f (x).
n - :
y ( n ) = f (x);
;
;
...............
,
.
,
.
, : (0) = 1/32, , .
. 1) :
;
; ;
.
2) 1, 2, 3, 4. :
, 1 = 0, 2 = 1/4, 3 = 0, 4 = 0. ,
.
, k 1
, k - 1 ,
. (2)
k , .. . (2)
.
z = f (x, 1, 2, ..., n -k ),
y(k) = f (x, 1, 2,.., n -k ) k - .
,
(2) = 1, .
. , .
1. . ,
.
. .
:
.
:
, .
.
.
, . z
(x 1)∙ C' (x) = x (x 1) C' (x) = x
.
(4), (3):
.
,
.
. , :
.
2. 1, 2. (2) = 1, :
, 1 = 3; 2 = 1/3. ,
.
,
, ,
|
|
. (5)
y ' = z. z : z = z (). z ():
;
;
..
(5), (n 1)- .
.
. , .
. , , :
.
. z ' = p
. :
.
= 0 . :
= z C 1.
p = z ', : z C 1. , .
z = y '. :
.
, :
.
= 0 z ' = 0, z = C y ' = C y = Cx + C 4 , 1, 2, 3.