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In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by . The Fabius function is defined on the unit interval, and is given by the probability distribution of : where the ''ξ''''n'' are independent uniformly distributed random variables on the unit interval. This function satisfies the functional equation ''f''′(''x'')=2''f''(2''x'') (where ''f''′ denotes the derivative of ''f'') for 0≤''x''≤1. There is a unique extension of ''f'' to the nonnegative real numbers which satisfies the same equation: it can be defined by ''f''(''x''+1) = 1−''f''(''x'') for 0≤''x''≤1 and ''f''(''x''+2''r'') = −''f''(''x'') for 0≤''x''≤2''r'' with ''r''≥1 integer; it is strongly related to the Thue–Morse sequence. ==References== 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「Fabius function」の詳細全文を読む スポンサード リンク
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