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In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration. Series acceleration techniques may also be used, for example, to obtain a variety of identities on special functions. Thus, the Euler transform applied to the hypergeometric series gives some of the classic, well-known hypergeometric series identities. == Definition == Given a sequence : having a limit : an accelerated series is a second sequence : which converges faster to than the original sequence, in the sense that : If the original sequence is divergent, the sequence transformation acts as an extrapolation method to the antilimit . The mappings from the original to the transformed series may be linear (as defined in the article sequence transformations), or non-linear. In general, the non-linear sequence transformations tend to be more powerful. 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「Series acceleration」の詳細全文を読む スポンサード リンク
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