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In mathematics, and more particularly in the analytic theory of regular continued fractions, an infinite regular continued fraction ''x'' is said to be ''restricted'', or composed of restricted partial quotients, if the sequence of denominators of its partial quotients is bounded; that is : and there is some positive integer ''M'' such that all the (integral) partial denominators ''ai'' are less than or equal to ''M''.〔For a fuller explanation of the K notation used here, please see this article.〕 ==Periodic continued fractions== A regular periodic continued fraction consists of a finite initial block of partial denominators followed by a repeating block; if : then ζ is a quadratic irrational number, and its representation as a regular continued fraction is periodic. Clearly any regular periodic continued fraction consists of restricted partial quotients, since none of the partial denominators can be greater than the largest of ''a''0 through ''a''''k''+''m''. Historically, mathematicians studied periodic continued fractions before considering the more general concept of restricted partial quotients. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Restricted partial quotients」の詳細全文を読む スポンサード リンク
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