Talk:Fundamental recurrence formulas

From Wikipedia, the free encyclopedia

[edit] Working backwards

If we arbitrarily set a0=1, then we can extend the recurrence relations backwards as is done for regular continued fractions:

\begin{align} h_{-2}& = 0& k_{-2}& = 1\\ h_{-1}& = 1& k_{-1}& = 0\\ h_0& = b_0& k_0& = 1\\ h_1& = b_1 b_0 + a_1 & k_1& = b_1\\ h_{n+1}& = b_{n+1} h_n + a_{n+1} h_{n-1} & k_{n+1}& = b_{n+1} k_n + a_{n+1} k_{n-1}\, \end{align}

What do you think? JRSpriggs 09:21, 16 December 2006 (UTC)