Sequence transformation

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a sequence transformation is an <a href="/facts/Operator_(mathematics)/1VWgEdjS">operator</a> acting on a given space of <a href="/facts/Sequence/gV2S4uqp">sequences</a> (a <a href="/facts/Sequence_space/2HkcM12K">sequence space</a>). Sequence transformations include <a href="/facts/Linear_mapping/Q1PBKNVV">linear mappings</a> such as <a href="/facts/Convolution/PVPrdz9J">discrete convolution</a> with another sequence and <a href="/facts/Resummation/IMpbTgRX">resummation</a> of a sequence and nonlinear mappings, more generally. They are commonly used for <a href="/facts/Series_acceleration/XmWMXVFh">series acceleration</a>, that is, for improving the <a href="/facts/Rate_of_convergence/JVGuzPoS">rate of convergence</a> of a slowly convergent sequence or <a href="/facts/Series_(mathematics)/yDnlsgIe">series</a>. Sequence transformations are also commonly used to compute the  <a href="/facts/Antilimit/pt0xS3Yb">antilimit</a> of a <a href="/facts/Divergent_series/c8Vjjjdx">divergent series</a> numerically, and are used in conjunction with <a href="/facts/Extrapolation_methods/wggUrqjF">extrapolation methods</a>.
</p><p>Classical examples for sequence transformations include the <a href="/facts/Binomial_transform/Wu345jgq">binomial transform</a>, <a href="/facts/M%25C3%25B6bius_transform/xDnSrPp6">Möbius transform</a>, and <a href="/facts/Stirling_transform/QYWYGXx0">Stirling transform</a>.
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Sequence transformation open-in-new

Sequence transformation