User:Grondilu/Möbius transformations: Difference between revisions
Content added Content deleted
(Created page with "This is a temporary page for a quick study on wp:Möbius transformations and continued fractions. <math>\mathrm{CF}_3(x) = a_0 + \cfrac{b_0}{a_1 + \cfrac{b_1}{a_2 +...") |
(initial conditions) |
||
Line 3: | Line 3: | ||
<math>\mathrm{CF}_3(x) = a_0 + \cfrac{b_0}{a_1 + \cfrac{b_1}{a_2 + \cfrac{b_1}{a_3 + \cfrac{b_3}{x}}}} = \frac{A_3+B_3x}{C_3+D_3x}</math> |
<math>\mathrm{CF}_3(x) = a_0 + \cfrac{b_0}{a_1 + \cfrac{b_1}{a_2 + \cfrac{b_1}{a_3 + \cfrac{b_3}{x}}}} = \frac{A_3+B_3x}{C_3+D_3x}</math> |
||
There is a recursive expression for <math>\mathrm{CF}_n</math>: |
There is a recursive expression for <math>\mathrm{CF}_n</math>: |
||
Line 18: | Line 17: | ||
--[[User:Grondilu|Grondilu]] 15:33, 3 January 2013 (UTC) |
--[[User:Grondilu|Grondilu]] 15:33, 3 January 2013 (UTC) |
||
Of course: |
|||
<math>\mathrm{CF}_0(x) = a_0 + \frac{b_0}{x} = \frac{b_0 + a_0 x}{x}</math> |
|||
Thus: |
|||
<math>A_0 = b_0,\quad B_0 = a_0\,\quad C_0 = 0,\quad D_0 = 1</math> |
|||
--[[User:Grondilu|Grondilu]] 01:49, 4 January 2013 (UTC) |
Latest revision as of 01:49, 4 January 2013
This is a temporary page for a quick study on Möbius transformations and continued fractions.
There is a recursive expression for :
It should lead to a recursive formula for :
And Thus:
--Grondilu 15:33, 3 January 2013 (UTC)
Of course:
Thus:
--Grondilu 01:49, 4 January 2013 (UTC)