翻訳と辞書 Words near each other ・ Gaussian units ・ Gaussian year ・ Gaussig House ・ Gaussiran Glacier ・ Gausson ・ Gausson (physics) ・ Gauss–Boaga projection ・ Gauss–Bonnet gravity ・ Gauss–Bonnet theorem ・ Gauss–Codazzi equations ・ Gauss–Hermite quadrature ・ Gauss–Jacobi quadrature ・ Gauss–Kronrod quadrature formula ・ Gauss–Krüger coordinate system ・ Gauss–Kuzmin distribution ・ Gauss–Kuzmin–Wirsing operator ・ Gauss–Laguerre quadrature ・ Gauss–Legendre algorithm ・ Gauss–Legendre method ・ Gauss–Lucas theorem ・ Gauss–Manin connection ・ Gauss–Markov ・ Gauss–Markov process ・ Gauss–Markov theorem ・ Gauss–Newton algorithm ・ Gauss–Seidel method ・ Gaustad ・ Gaustad (station) ・ Gaustad Hospital ・ Gaustadalléen (station) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gauss–Kuzmin–Wirsing operator ： ウィキペディア英語版 :''"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:h(x)=1/x-\lfloor 1/x \rfloor.\,This operator acts on functions as:()(x) = \sum_^\infty \frac f \left(\frac \right).The first eigenfunction of this operator is:\frac 1\ \frac 1which 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: x=()\,is the continued fraction representation of a number 0 : h(x)=().\,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. :''"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 :$h(x)=1/x-\backslash lfloor\; 1/x\; \backslash rfloor.\backslash ,$ This operator acts on functions as :$()(x)\; =\; \backslash sum\_^\backslash infty\; \backslash frac\; f\; \backslash left(\backslash frac\; \backslash right).$ The first eigenfunction of this operator is :$\backslash frac\; 1\backslash \; \backslash frac\; 1$ 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 : $x=()\backslash ,$ is the continued fraction representation of a number 0 < ''x'' < 1, then : $h(x)=().\backslash ,$ 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『 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:h(x)=1/x-\lfloor 1/x \rfloor.\,This operator acts on functions as:()(x) = \sum_^\infty \frac f \left(\frac \right).The first eigenfunction of this operator is:\frac 1\ \frac 1which 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: x=()\,is the continued fraction representation of a number 0 : h(x)=().\,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.">ウィキペディア（Wikipedia）』 ■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:h(x)=1/x-\lfloor 1/x \rfloor.\,This operator acts on functions as:()(x) = \sum_^\infty \frac f \left(\frac \right).The first eigenfunction of this operator is:\frac 1\ \frac 1which 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: x=()\,is the continued fraction representation of a number 0 : h(x)=().\,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.">ウィキペディアで「:''"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:h(x)=1/x-\lfloor 1/x \rfloor.\,This operator acts on functions as:()(x) = \sum_^\infty \frac f \left(\frac \right).The first eigenfunction of this operator is:\frac 1\ \frac 1which 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: x=()\,is the continued fraction representation of a number 0 : h(x)=().\,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.」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.