. w = f (z) D, . L z 0, D . z, L, . : (
| z z 0| < | t z 0|, ) , , : , . ,
.
- f (z). L, L , D.
. f (z) . ; ,
. .
. k f (z), f (a) = f ′(a) = f ″(a) =... = f (k −1)(a) = 0, f (k)(a) ≠ 0.
. . a = 0 - , f (0) = 0. :
f ″(z) = − sin z + z, f ″(0)= 0,
f (3)(z) = − cos z + 1, f (3)(0) = 0,
f (4)(z) = sin z, f (4)(0) = 0,
f (5)(z) = cos z, f (5)(0) = 1 ≠ 0,. a = 0 - , - .
. .
z f (z), f (z) () { z:0<| z a |< }, .
f (z), f (z) { R <| z |< } z=
= 0 .
f (z) .
f (z)
) ,
) ,
) ,
.
, . .
(f(z) - - ).
c-1 - z-1 f(z) .
1. - :
- :
,
2. - m:
3. f(z) -
f(z) zk, k = 1, 2,..., n, ,