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In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants :''R''''m'', ''n'' to a given complex formal power series. Certain sequences of approximants lying within a Padé table can often be shown to correspond with successive convergents of a continued fraction representation of a holomorphic or meromorphic function. ==History== Although earlier mathematicians had obtained sporadic results involving sequences of rational approximations to transcendental functions, Frobenius (in 1881) was apparently the first to organize the approximants in the form of a table. Henri Padé further expanded this notion in his doctoral thesis ''Sur la representation approchee d'une fonction par des fractions rationelles'', in 1892. Over the ensuing 16 years Padé published 28 additional papers exploring the properties of his table, and relating the table to analytic continued fractions. Modern interest in Padé tables was revived by H. S. Wall and Oskar Perron, who were primarily interested in the connections between the tables and certain classes of continued fractions. Daniel Shanks and Peter Wynn published influential papers about 1955, and W. B. Gragg obtained far-reaching convergence results during the '70s. More recently, the widespread use of electronic computers has stimulated a great deal of additional interest in the subject.〔Jones and Thron, 1980.〕 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「Padé table」の詳細全文を読む スポンサード リンク
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