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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Double exponential function ： ウィキペディア英語版 Double exponential function A double exponential function is a constant raised to the power of an exponential function. The general formula is $f(x)\; =\; a^=a^$, which grows much more quickly than an exponential function. For example, if ''a'' = ''b'' = 10: *''f''(0) = 10 *''f''(1) = 1010 *''f''(2) = 10100 = googol *''f''(3) = 101000 *''f''(100) = 1010100 = googolplex. Factorials grow faster than exponential functions, but much slower than doubly exponential functions. Tetration and the Ackermann function grow even faster. See Big O notation for a comparison of the rate of growth of various functions. The inverse of the double exponential function is the double logarithm ln(ln(''x'')). ==Doubly exponential sequences== Aho and Sloane observed that in several important integer sequences, each term is a constant plus the square of the previous term, and show that such sequences can be formed by rounding to the nearest integer the values of a doubly exponential function in which the middle exponent is two.〔.〕 Integer sequences with this squaring behavior include * The Fermat numbers ::$F(m)\; =\; 2^+1$ * The harmonic primes: The primes p, in which the sequence 1/2+1/3+1/5+1/7+....+1/p exceeds 0,1,2,3,.... :The first few numbers, starting with 0, are 2,5,277,5195977,... * The Double Mersenne numbers ::$MM(p)\; =\; 2^-1$ * The elements of Sylvester's sequence ::$s\_n\; =\; \backslash left\backslash lfloor\; E^$ More generally, if the ''n''th value of an integer sequences is proportional to a double exponential function of ''n'', Ionascu and Stanica call the sequence "almost doubly-exponential" and describe conditions under which it can be defined as the floor of a doubly exponential sequence plus a constant.〔.〕 Additional sequences of this type include * The prime numbers 2, 11, 1361, ... ::$a(n)\; =\; \backslash left\backslash lfloor\; A^\backslash right\backslash rfloor$ :where ''A'' ≈ 1.306377883863 is Mills' constant. 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「Double exponential function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.