翻訳と辞書 Words near each other ・ Theudebald (disambiguation) ・ Theta correspondence ・ Theta Crateris ・ Theta criterion ・ Theta Crucis ・ Theta Cygni ・ Theta defensin ・ Theta Delphini ・ Theta Delta Chi ・ Theta Delta Kappa ・ Theta Delta Sigma ・ Theta divisor ・ Theta Doradus ・ Theta Draconis ・ Theta Eridani ・ Theta function ・ Theta function (disambiguation) ・ Theta function of a lattice ・ Theta Geminorum ・ Theta graph ・ Theta group ・ Theta Gruis ・ Theta Herculis ・ Theta Hydrae ・ Theta Indi ・ Theta Island, Bermuda ・ Theta Islands ・ Theta Kappa Nu ・ Theta Kappa Omega ・ Theta Kappa Pi 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 Theta function ： ウィキペディア英語版 Theta function In mathematics, theta functions are special functions of several complex variables. They are important in many areas, including the theories of abelian varieties and moduli spaces, and of quadratic forms. They have also been applied to soliton theory. When generalized to a Grassmann algebra, they also appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called ''z''), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function. In the abstract theory this comes from a line bundle condition of descent. ==Jacobi theta function== There are several closely related functions called Jacobi theta functions, and many different and incompatible systems of notation for them. One Jacobi theta function (named after Carl Gustav Jacob Jacobi) is a function defined for two complex variables ''z'' and τ, where ''z'' can be any complex number and τ is confined to the upper half-plane, which means it has positive imaginary part. It is given by the formula :$$ \vartheta(z; \tau) = \sum_^\infty \exp (\pi i n^2 \tau + 2 \pi i n z) = 1 + 2 \sum_^\infty \left(e^\right)^ \cos(2\pi n z) = \sum_^\infty q^\eta^n where ''q'' = exp(π''i''τ) and η = exp(2π''iz''). It is a Jacobi form. If τ is fixed, this becomes a Fourier series for a periodic entire function of ''z'' with period 1; in this case, the theta function satisfies the identity :$\backslash vartheta(z+1;\; \backslash tau)\; =\; \backslash vartheta(z;\; \backslash tau).$ The function also behaves very regularly with respect to its quasi-period τ and satisfies the functional equation :$\backslash vartheta(z+a+b\backslash tau;\backslash tau)\; =\; \backslash exp(-\backslash pi\; i\; b^2\; \backslash tau\; -2\; \backslash pi\; i\; b\; z)\backslash ,\backslash vartheta(z;\backslash tau)$ where ''a'' and ''b'' are integers. 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「Theta 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.