https://wiki.lojban.io/index.php?action=history&feed=atom&title=ne%27o%27aune'o'au - Revision history2026-04-28T12:01:43ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=ne%27o%27au&diff=11500&oldid=prevNalvaizmiku: Import words via API2026-01-13T15:50:35Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
ne'o'au<br />
==== type ====<br />
experimental cmavo<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Tue Dec 13 21:46:07 2022<br />
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== English ==<br />
=== Definition #73055 - Preferred ===<br />
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==== selma'o ====<br />
VUhU3<br />
==== definition ====<br />
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mekso quaternary operator: polygamma function; for 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>, outputs the <span class="MATH">(- <i>X</i><sub>2</sub>)</span>th derivative of Log(ne'o'a( MATH<br />
$X_1, X_3, X_4$<br />
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<span class="MATH"><i>X</i><sub>1</sub>, <i>X</i><sub>3</sub>, <i>X</i><sub>4</sub></span>)) with respect to <span class="MATH"><i>X</i><sub>1</sub></span>.<br />
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==== notes ====<br />
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By default, <span class="MATH"><i>X</i><sub>2</sub> = - 1</span> (notice the double-negative). Inherits the defaults for/of "[[ne'o'a|ne'o'a]]" (for: <span class="MATH"><i>X</i><sub>3</sub> =</span> ne'o'a<span class="MATH"><sub>2</sub></span>, and <span class="MATH"><i>X</i><sub>4</sub> =</span> ne'o'a<span class="MATH"><sub>3</sub></span>). The 0th derivative is the identity operator; in order to be consistent with "[[salri|salri]]", negative-integer-order derivatives (meaning: positive <span class="MATH"><i>X</i><sub>2</sub></span>) are antiderivatives. <span class="MATH"><i>X</i><sub>2</sub></span> being other than a non-positive integer, or <span class="MATH"><i>X</i><sub>1</sub></span> being non-real, should require mention or assumption of the cultural default interpretation of the definition of the differintegral operator. "Log" here denotes the primary branch of the natural (base-<span class="MATH"><i>e</i></span>) logarithm. This is a shift of the polygamma function by 1, so as to be consistent with "[[ne'o|ne'o]]". Therefore, the basic digamma function (derived from the gamma, not Pi, function), often denoted "psi<span class="MATH"><sub>0</sub>(<i>z</i>)</span>, is equal to this word's output for MATH<br />
$X_1 = z - 1, X_2 = -1, X_3 = 0, X_4 =$<br />
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<span class="MATH"><i>X</i><sub>1</sub> = <i>z</i> - 1, <i>X</i><sub>2</sub> = - 1, <i>X</i><sub>3</sub> = 0, <i>X</i><sub>4</sub> =</span> +infty (notice the prevalence of the default parameter values).<br />
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==== gloss words ====<br />
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<ul><li>[[natlang/en/digamma function|digamma function]]</li><li>[[natlang/en/polyfactorial|polyfactorial]]</li><li>[[natlang/en/polygamma function|polygamma function]]</li><li>[[natlang/en/poly-pi function|poly-pi function ; related to the factorial]]</li></ul><br />
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==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
1<br />
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==== time ====<br />
Tue Dec 13 22:04:30 2022<br />
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<br/><font size="+1">Examples</font><br />
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=== Etymology ===</div>Nalvaizmiku