( )
16
: .
:
2011/12 .
..3
..9
.
f(x) , , , . , f(x), : f(x) , , f(x) .
, . , .
f(x). , f(x) . . f(x) (. . 1). - f(x), .
f (x), , , . .
:
1) , , .
2) f (x) , f (ax) .
3) f (x)- , , ( ), . . a b .
.
f (x) :
(1)
, :
, n =1,2,...
(1) , .
, .
1 (). 1- [ ] , f (x) , f (x) ( -).
|
|
2. f (x) , [ ] , f (x) ( -).
f (x) - 2 L, f (- x) = f (x).
:
=
=
= 0 , n =1,2,...
, , 2 L :
f (x) - 2 L, f (- x) = - f (x).
:
, n =1,2,...
, , 2 L :
f (x)
, ,
,
,
f (x) [0 ,L ], f (x) [- L, 0]; (T =2 L), , .
, [ a, b ], : [ b, a +2 L ] , [ b -2 L, a ] .
f (x),
,
:
(n =1,2,...)
T = 2L | |
g (x) 2π:
2 L:
, f (x) 2 L 2π, :
|
.
, f (x) , :
1)
(.. )
2) [- L, L ] -
|
|
3) , , f (x)
f(x) :
, ,
.