https://wiki.lojban.io/index.php?action=history&feed=atom&title=cia%27o%27ecia'o'e - Revision history2026-05-07T08:10:16ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=cia%27o%27e&diff=2332&oldid=prevNalvaizmiku: Import words via API2026-01-13T14:30:32Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
cia'o'e<br />
==== type ====<br />
obsolete cmavo<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Wed Oct 15 04:54:36 2014<br />
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== English ==<br />
=== Definition #60539 - Preferred ===<br />
<br />
==== selma'o ====<br />
VUhU<br />
==== definition ====<br />
mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.<br />
==== notes ====<br />
<br />
Usually denoted MATH<br />
$Y^m_l (\theta, \phi)$<br />
<br />
<span class="MATH"><i>Y</i><sup>m</sup><sub>l</sub>(<i>θ</i>, <i>φ</i>)</span>. The Condon-Shortley phase must be prepended to the definition. The normalization is chosen so that the integral over all (solid) angles of MATH<br />
$Y^m_l(\Omega) conj(Y^n_k(\Omega) = \delta(m,n) \delta(l,k)$<br />
<br />
<span class="MATH"><i>Y</i><sup>m</sup><sub>l</sub>(<i>Ω</i>)<i>conj</i>(<i>Y</i><sup>n</sup><sub>k</sub>(<i>Ω</i>) = <i>δ</i>(<i>m</i>, <i>n</i>)<i>δ</i>(<i>l</i>, <i>k</i>)</span>.<br />
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==== gloss words ====<br />
<br />
<ul><li>[[natlang/en/spherical harmonics|spherical harmonics]]</li></ul><br />
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==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
1<br />
<br />
==== time ====<br />
Wed Oct 15 04:54:36 2014<br />
<br />
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<br/><font size="+1">Examples</font><br />
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=== Etymology ===</div>Nalvaizmiku