Complete Quotient

In the metrical theory of regular continued fractions, the kth complete quotient ζ k is obtained by ignoring the first k partial denominators ai. For example, if a regular continued fraction is given by

x = = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{\ddots}}}},

then the successive complete quotients ζ k are given by

\begin{align} \zeta_0 & = \\ \zeta_1 & = \\ \zeta_2 & = \\ \zeta_k & = . \, \end{align}

Read more about Complete Quotient:  A Recursive Relationship, Complete Quotients and The Convergents of x

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