https://wiki.lojban.io/index.php?action=history&feed=atom&title=tei%27autei'au - Revision history2026-05-01T23:08:31ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=tei%27au&diff=18604&oldid=prevNalvaizmiku: Import words via API2026-01-13T16:50:18Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
tei'au<br />
==== type ====<br />
experimental cmavo<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Wed Apr 25 04:45:05 2018<br />
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== English ==<br />
=== Definition #70638 - Preferred ===<br />
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==== selma'o ====<br />
VUhU<br />
==== definition ====<br />
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4-ary mekso operator: Taylor expansion/polynomial term; for ordered input MATH<br />
$(X_1, X_2, X_3, X_4)$<br />
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<span class="MATH">(<i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>, <i>X</i><sub>3</sub>, <i>X</i><sub>4</sub>)</span>, output is the <span class="MATH"><i>X</i><sub>3</sub></span>th Taylor polynomial term of at-least-<span class="MATH"><i>X</i><sub>3</sub></span>-smooth function <span class="MATH"><i>X</i><sub>2</sub></span> which was expanded around point <span class="MATH"><i>X</i><sub>4</sub></span> and which is evaluated at point <span class="MATH"><i>X</i><sub>1</sub></span>, namely MATH<br />
$(1/(X_3!)) * (D^{X_3}(X_2))(X_4) * (X_1-X_4)^{X_3}$<br />
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<span class="MATH">(1/(<i>X</i><sub>3</sub>!))*(<i>D</i><sup>X<sub>3</sub></sup>(<i>X</i><sub>2</sub>))(<i>X</i><sub>4</sub>)*(<i>X</i><sub>1</sub> - <i>X</i><sub>4</sub>)<sup>X<sub>3</sub></sup></span>.<br />
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==== notes ====<br />
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All of the usual assumptions must apply in order to be well-defined. <span class="MATH"><i>X</i><sub>3</sub></span> must be a nonnegative integer. <span class="MATH"><i>X</i><sub>2</sub></span> must be a function with at least <span class="MATH"><i>X</i><sub>3</sub></span> derivatives on the interval disc/interval defined by <span class="MATH"><i>X</i><sub>1</sub></span> and <span class="MATH"><i>X</i><sub>4</sub></span> such that said derivative takes values for which the other operators make sense (and finity is usually assumed). <span class="MATH"><i>X</i><sub>1</sub></span> and <span class="MATH"><i>X</i><sub>4</sub></span> must be elements of the domain of <span class="MATH"><i>X</i><sub>2</sub></span> (and the <span class="MATH"><i>X</i><sub>3</sub></span>th derivative thereof in the latter case). The notation " MATH<br />
$(D^<a class="undefined" href="../dict/X_3?bg=1;langidarg=2">X_3</a>(X_2))(X_4)$<br />
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<span class="MATH">(<i>D</i><sup>X<sub>3</sub></sup>(<i>X</i><sub>2</sub>))(<i>X</i><sub>4</sub>)</span>" represents the <span class="MATH"><i>X</i><sub>3</sub></span>th derivative of <span class="MATH"><i>X</i><sub>2</sub></span>, applied to <span class="MATH"><i>X</i><sub>4</sub></span>; the "<span class="MATH">!</span>" notation represents the factorial.<br />
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==== gloss words ====<br />
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<ul><li>[[natlang/en/Taylor expansion term|Taylor expansion term]]</li><li>[[natlang/en/Taylor polynomial term|Taylor polynomial term]]</li><li>[[natlang/en/Taylor term|Taylor term]]</li></ul><br />
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==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
1<br />
<br />
==== time ====<br />
Wed Apr 25 04:47:16 2018<br />
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[[comments.html?valsi=32183;definition=70638|[View<br />
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<br/><font size="+1">Examples</font><br />
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=== Etymology ===</div>Nalvaizmiku