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In mathematics, the Siegel G-functions are a class of functions in transcendental number theory introduced by C. L. Siegel. They satisfy a linear differential equation with polynomial coefficients, and the coefficients of their power series expansion lie in a fixed algebraic number field and have heights of at most exponential growth. ==Definition== A Siegel G-function is a function given by an infinite power series : where the coefficients ''an'' all belong to the same algebraic number field, ''K'', and with the following two properties. # ''f'' is the solution to a linear differential equation with coefficients that are polynomials in ''z''; # the projective height of the first ''n'' coefficients is ''O''(''cn'') for some fixed constant ''c'' > 0. The second condition means the coefficients of ''f'' grow no faster than a geometric series. Indeed, the functions can be considered as generalisations of geometric series, whence the name G-function, just as E-functions are generalisations of the exponential function. 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「Siegel G-function」の詳細全文を読む スポンサード リンク
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