User:Grondilu/Möbius transformations: Difference between revisions
User:Grondilu/Möbius transformations (view source)
Revision as of 01:49, 4 January 2013
, 11 years agoinitial conditions
(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 +...") |
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<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>:
Line 18 ⟶ 17:
--[[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)
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