continued fraction images
TRANSCRIPT
-
7/27/2019 Continued Fraction Images
1/8
Images of ContinuedImages of ContinuedImages of ContinuedImages of Continued Fraction Expansions IFraction Expansions IFraction Expansions IFraction Expansions I
2012
. (). n
, ,
.
z ( )f z , , .
11 2 3 2 5 2
z z z z z z ze = +
+ + + 5, 10, 20, 40 .
20 , 20x y .
-
7/27/2019 Continued Fraction Images
2/8
( ) z
f z e= 20 , 20x y .
2 2 2 2 2 2
1 2 3tan( )
1 3 5 7
z z z zArc z =
+ + + +
.
10, 100. 10 , 10x y . .
-
7/27/2019 Continued Fraction Images
3/8
2 2 2 2 2 2
1 2 1 2 3
1 1 3 5 7
z z z z zLn
z
+ =
10 , 10x y . 10,
100. 1 1, ( ) .
.
2 2 2
( )1 3 5 7
z z z zTan z =
z ( )
5 100. 10 , 10x y .
, ( )Tan z = .
-
7/27/2019 Continued Fraction Images
4/8
1 1 2 2 3 3(1 ) (1 ) (1 )
( )1 1 1 1
z z z z z z zF z
=
1n
n = . ()
( )1( )
1
n n
n
z zT w
w
=
. 5,
100 12 , 12x y . ( ) z R
.
1 1 2 2 3 3(1 ) (1 ) (1 )( )1 1 1
z z z z z zF z =
, 50, 20 , 20x y . 1nn
= .
-
7/27/2019 Continued Fraction Images
5/8
1 2 3
( )1 2 3
z z zF z
z z z
=
+ + + , . 50. 70 , 70x y
50. 25 , 25x y .
1 1 1 2 2 3 3
( )1 1 1
a a aF z
z z z z
=
+ + + + + + +,
. 0. , 5 , 50. 1.5 , 1.5x y .
-
7/27/2019 Continued Fraction Images
6/8
( ) ( ) ( ) ( )1) 2 2 1 3 3 1) 4 4 1
( )1 1 1 1
z z z z z z z zF z
+ + =
+ + + +, 50n = , 3 , 3x y .
( ) ( ) ( ) ( )1 2 3 41
( )1 1 1 1 1
i z i z i z i zF z
+ + + +=
+ + + + + , 100, 3 , 3x y .
( )1.1491 1 i = + .
-
7/27/2019 Continued Fraction Images
7/8
( ) , 1z z z
F z z iz z z
= + = ++ + + + + +
. 50n = , 4 , 4x y .
1.0769(1 )i = + .
2 2 2 2 2 2
1 1 1 1 2 2 3 3(1 )
1 2 3 4 5 6 7
z z z z z zLn z
z+ =
+ + + + + + + , 6 , 6x y 100n = .
1, 1.
( ) 3.2331 .
-
7/27/2019 Continued Fraction Images
8/8
. , . , , (1980)
. , , . . . . . (2012)