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Complete quotient
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Complete quotient : ウィキペディア英語版
Complete quotient
In the metrical theory of regular continued fractions, the ''k''th complete quotient ζ ''k'' is obtained by ignoring the first ''k'' partial denominators ''a''''i''. For example, if a regular continued fraction is given by
:
x = (a_1, a_2, a_3, \dots ) = a_0 + \cfrac}}},

then the successive complete quotients ζ ''k'' are given by
:
\begin
\zeta_0 & = (a_1, a_2, a_3, \dots )\\
\zeta_1 & = (a_2, a_3, a_4, \dots )\\
\zeta_2 & = (a_3, a_4, a_5, \dots )\\
\zeta_k & = (a_, a_, a_, \dots ). \,
\end

==A recursive relationship==
From the definition given above we can immediately deduce that
:
\zeta_k = a_k + \frac ), \,

or, equivalently,
:
\zeta_ = \frac.\,


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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