CF equivalence transformations

    \[b_0+\mathbf{K}(a_n/b_n) \To b_0+\mathbf{K} (1/d_n)\]

where d_n=b_n \prod\limits_{k=1}^n {{a}_k^{(-1)}}^{n+1-k} for n=1,2,3\dots
i.e. d_n has the form:

    \begin{align*} && &&1 &&2 &&3 &&4 &&5 &&\\ &&d: &&\frac{b_1}{a_1}&&b_2\frac{a_1}{a_2} &&b_3\frac{a_2}{a_1a_3}&&b_4\frac{a_1a_3}{a_2a_4} &&b_5\frac{a_2a_4}{a_1a_3a_5}&&\dots \end{align*}

references

Lorentzen, Waadeland – Continued fractions with applications, p74-5

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