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:''"GKW" redirects here. For the Indian engineering firm see Guest Keen Williams. In mathematics, the Gauss–Kuzmin–Wirsing operator, named after Carl Gauss, Rodion Osievich Kuzmin and Eduard Wirsing, occurs in the study of continued fractions; it is also related to the Riemann zeta function. ==Introduction== The Gauss–Kuzmin–Wirsing operator is the transfer operator of the Gauss map : This operator acts on functions as : The first eigenfunction of this operator is : which corresponds to an eigenvalue of ''λ''1=1. This eigenfunction gives the probability of the occurrence of a given integer in a continued fraction expansion, and is known as the Gauss–Kuzmin distribution. This follows in part because the Gauss map acts as a truncating shift operator for the continued fractions: if : is the continued fraction representation of a number 0 < ''x'' < 1, then : Additional eigenvalues can be computed numerically; the next eigenvalue is ''λ''2 = −0.3036630029... and its absolute value is known as the Gauss–Kuzmin–Wirsing constant. Analytic forms for additional eigenfunctions are not known. It is not known if the eigenvalues are irrational. 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「Gauss–Kuzmin–Wirsing operator」の詳細全文を読む スポンサード リンク
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