8/13/2019 Zeno Contours, Parametric Forms & Integrals
1/11
2013
: , , ,
: 1. , ,( ) ( )k n k ng z z z = + z S , ( )k ng z S
S . ,
lim 0k n
n
= , () 1,2,...,k n= .
1, 1,( ) ( )n nG z g z= , ( ), , 1,( ) ( )k n k n k nG z g G z=
,( ) ( )n n nG z G z= ( ) lim ( )n
nG z G z
= ,
. .
0,1. , ( ) ( )z f z z = , f=F .
( )
=
=LLLL .
. ,
1 =k n
n
,
1( ) ( ) +k ng z z z
n ( ) z S,
,( )k nz S g z S .
, 1, 2, 1,
1 1 1 1( ) ( ) ( ( )) ( ( )) ( ( ))
= + + + + +n n n n n nG z z z G z G z G z
n n n n.
,
( ) [ ] ( ) ( )1
1,
0
, , 0,1 and , lim ( ) , with , defined
mk mnm
kz t t z G z z t dt
n:
1
0
1 1 1 2 1 3 1( ) , , , , ( , )
= + + + +
n
nG z z z z z z z t dt
n n n n n n n n
, ( , ) lim ( , )
=r
rt t
z t z t .
( )
. ( )
.
