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( )
xT
n
n
( )
( )
( )
−++−−=
nn
n
xxxxxT 11
2
1
22
(63)
(61)
,
n
1
+
n
() ( ) ( )
( ) ( )
=
+−−
−⋅=⋅−
−⋅=+=+=
+
2
1cos1cos
coscossinsin
coscoscos1cos
1
unun
unuunu
uunununuxT
n
( )
( )
( )
2
2
11
xTxT
xxT
nn
n
+−
+−=
( ) ( ) ( )
xTxxTxT
nnn 11
2
−+
−=
(64)
(64) (62)
.52016,188
,34,12,,1
35
5
24
4
3
3
2
210
xxxTxxT
xxTxTxTT
+−=+−=
−=−===
(65)
Maple 9.5, 4
4.
( ) ( ) ( ) ( ) ( )
.,,,,
43210
xTxTxTxTxT
0
T
1
T
2
T
3
T
4
T
Tn ( x )
n
Tn ( x ) =
1
2
x (
− x 2
− 1
n
+ x ) (
+ x 2
− 1
n
) (63)
(61)
, n n +1
Tn+1 ( x ) = cos u (n + 1) = cos(nu + u ) = cos nu ⋅ cos u −
cos(n − 1)u − cos(n + 1)u
− sin nu ⋅ sin u = cos nu ⋅ cos u − =
2
Tn−1 ( x ) Tn+1 ( x )
= xTn ( x ) − +
2 2
Tn +1 ( x ) = 2 xTn ( x ) − Tn−1 ( x ) (64)
(64) (62)
T0 = 1, T1 = x, T2 = 2 x 2 − 1, T3 = 4 x 3 − 3x,
(65)
T4 = 8 x 4 − 8 x 2 + 1, T5 = 16 x 5 − 20 x 3 + 5 x.
Maple 9.5, 4
T0
T1
T3 T4
T2
4.
T0 ( x ), T1 ( x ), T2 ( x ) , T3 ( x ) , T4 ( x ) .
