Editing Xi (letter)

{{Short description|Fourteenth letter in the Greek alphabet}}
{{Distinguish|text="≡", the [[triple bar]] character, the Cyrillic letter [[Ksi (Cyrillic)|ksi]] (Ѯ), or the Arabic letter [[ع]]}}
{{Distinguish|Chi (letter)}}
{{More citations needed|date=June 2010}}
{{Greek Alphabet|letter=xi}}

'''Xi''' ({{IPAc-en|z|aɪ|audio=LL-Q1860 (eng)-Flame, not lame-Xi.wav}} {{respell|ZY}} or {{IPAc-en|(|k|)|s|aɪ}} {{respell|(K)SY}};<ref>{{OED|xi}}</ref><ref>"xi". ''New Oxford American Dictionary'', 2nd Edition.</ref> uppercase '''Ξ''', lowercase '''ξ'''; {{langx|el|ξι}}) is the fourteenth letter of the [[Greek alphabet]], representing the voiceless [[consonant cluster]] {{IPA|el|ks|}}. Its name is pronounced {{IPA|el|ksi|}} in [[Modern Greek]]. In the system of [[Greek numerals]], it has a value of 60. Xi was derived from the [[Phoenician alphabet|Phoenician letter]] [[samekh]] [[Image:Phoenician samekh.svg|20px]].

Xi is distinct from the letter [[chi (letter)|chi]], which gave its form to the Latin letter [[X]].

==Greek ==
[[Image:Xi alternate.png|thumb|upright 1.5|left|A joined variant of Ξ (''New Athena Unicode'' font)]]
Both in classical [[Ancient Greek]] and in [[Modern Greek]], the letter Ξ represents the consonant cluster /ks/. In some [[Archaic Greek alphabets|archaic local variants]] of the Greek alphabet, this letter was missing. Instead, especially in the dialects of most of the Greek mainland and [[Euboea]], the cluster /ks/ was represented by Χ (which in classical Greek is [[Chi (letter)|chi]], used for {{IPA|/kʰ/}}).

Because this variant of the Greek alphabet was used in [[Magna Graecia]] (the Greek colonies in [[Sicily]] and the southern part of the [[Italian peninsula]]), the [[Latin alphabet]] borrowed Χ rather than Ξ as the Latin letter that represented the /ks/ cluster that was also present in Latin.

==Cyrillic==
Xi was adopted into the [[early Cyrillic alphabet]] as the letter [[Ksi (Cyrillic letter)|ksi]] (Ѯ&nbsp;ѯ). It was ultimately removed from the [[Russian alphabet]] in 1735.

==Mathematics and science==

===Uppercase===
The uppercase letter Ξ is used as a symbol in various contexts.

==== Pure mathematics ====
* [[Harish-Chandra's Ξ function]] in [[harmonic analysis]] and [[representation theory]]
* The [[Riemann Xi function]] in [[analytic number theory]] and [[complex analysis]]

==== Physics ====
* The "[[Xi baryon|cascade particles]]" in particle physics
* The [[Partition function (statistical mechanics)|partition function]] under the [[grand canonical ensemble]] in statistical mechanics

==== Other uses ====
* Indicating "no change of state" in [[Z notation]] in [[computing]]
* Used as the [[Latin]] letter [[E]] in some logos.
* Monetary units of the [[cryptocurrency|cryptocurrencies]] [[Ethereum#Ether|Ether]] (and less commonly [[Ethereum Classic|ETC]]), equal to 10<sup>18</sup> Wei

===Lowercase===
The lowercase letter ξ is used as a symbol for:

==== Pure mathematics ====
* [[Random variable]]s
* A parameter in a [[generalized Pareto distribution]]
* The symmetric function equation of the [[Riemann zeta function]] in mathematics, also known as the [[Riemann xi function]]
* A [[universal set]] in [[set theory]]
* A number used in the remainder term of [[Taylor's theorem]] that falls between the limits ''a'' and ''b''
* A number used in error approximations for formulas that are applications of Taylor's theorem, such as [[Newton–Cotes formulas]]

==== Physics and astronomy ====
* In fluid dynamics, the [[Iribarren parameter]].<ref>{{Cite book |title=Coastal risk management in a changing climate |date=2015 |publisher=Butterworth-Heinemann |isbn=978-0-12-397310-8 |editor-last=Zanuttigh |editor-first=Barbara |location=Amsterdam |page=130 |quote=...where ''ξ{{sub|p}}'' is the Iribarren parameter,...}}</ref>
* The [[initial mass function]] in [[astronomy]].<ref>{{Cite book |last1=Corbelli |first1=Edvige |title=The initial mass function 50 years later |last2=Palla |first2=Francesco |last3=Zinnecker |first3=Hans |date=2005 |publisher=Springer |isbn=978-1-4020-3406-0 |series=Astrophysics and space science library |location=Dordrecht |page=175 |quote=...where ''ξ(m)'' is the stellar initial mass function (IMF).}}</ref>
* The [[correlation function (astronomy)|correlation function]] in [[astronomy]].<ref>{{Cite book |title=Encyclopedia of astronomy and astrophysics |date=1989 |publisher=Acad. Pr |isbn=978-0-12-226690-4 |editor-last=Meyers |editor-first=Robert A. |location=San Diego, Calif. |page=4 |quote=The observations above reveal that ''ξ(r)'' is well represented by a power law of the form…}}</ref>
* [[Spatial frequency]];<ref>SPIE Optipedia article: [http://spie.org/x34301.xml "Spatial Frequency"]</ref>  also sometimes temporal [[frequency]].
* A small displacement in MHD [[plasma stability]] theory
* The x-coordinate of computational space as used in [[computational fluid dynamics]]
* [[Electric potential energy|Potential difference]] in physics (in volts)
* The radial integral in the spin-orbit matrix operator in [[atomic physics]].
* The [[Killing vector field|Killing vector]] in general relativity.<ref>{{Cite book |last1=Peter |first1=Patrick |url=https://www.worldcat.org/title/313665248 |title=Primordial cosmology |last2=Uzan |first2=Jean-Philippe |date=2009 |publisher=Oxford University Press |isbn=978-0-19-920991-0 |edition=1st |location=Oxford ; New York |page=168 |oclc=313665248 |quote=As explained in Chapter 1, the continuous symmetry can be characterized by a Killing vector field, ''ξ'',...}}</ref>
* Average logarithmic energy decrement per collision (neutron calculations in nuclear physics)<ref>{{Cite book |last=Bodansky |first=David |title=Nuclear Energy: Principles, Practices, and Prospects |date=2008 |publisher=Springer New York |isbn=978-0-387-20778-0 |edition=2nd |location=New York, NY |page=159 |quote=The mean logarithmic energy decrement ''ξ'' is defined as…}}</ref>
* [[Pippard's cohesion length]] in [[superconductors]]
* The diameter of a crystal nucleus in [[nucleation]] theory
* [[Microturbulence]] velocity in a stellar atmosphere
* The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics.
* Dimensionless distance variable used in the [[Lane–Emden equation]]

==== Other uses ====
* Propositional variables in some philosophical works, first found in Wittgenstein's [[Tractatus Logico-Philosophicus|Tractatus]]
* [[Extent of reaction]], a concept in [[physical chemistry]]<ref>IUPAC Gold Book Entry: [http://goldbook.iupac.org/E02283.html "Extent of Reaction"] {{webarchive |url=https://web.archive.org/web/20120629101118/http://goldbook.iupac.org/E02283.html |date=June 29, 2012 }}</ref> used often in [[chemical engineering]] kinetics and [[thermochemistry]]
* Unknown [[stereochemistry]] or [[stereocentre]] configuration in a planar [[ring (chemistry)|ring system]] in [[organic chemistry]],<ref name="BuckinghamCooper2015">{{cite book|first1=John|last1=Buckingham|first2=Caroline M.|last2=Cooper|first3=Rupert|last3=Purchase|title=Natural Products Desk Reference|url=https://books.google.com/books?id=n4zwCgAAQBAJ&pg=PA53|date=18 November 2015|publisher=CRC Press|isbn=978-1-4398-7362-5|pages=53–}}</ref> as well as uppercase Xi for unknown ''R''/''S''/''E''/''Z'' configuration in general<ref>{{cite book|title=Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names|year=2014|pages=1159–1160|publisher=Royal Society of Chemistry |isbn=9780854041824|url=https://books.google.com/books?id=4USgAgAAQBAJ&pg=1160|access-date=11 September 2017}}</ref>
* One of the two different polypeptide chains of the human embryonic [[hemoglobin]] types Hb-Portland (ξ<sub>2</sub>γ<sub>2</sub>) and Hb-Gower I (ξ<sub>2</sub>ε<sub>2</sub>)
* A parameter denoted as [[warped time]] used to derive the equations for homogeneous [[azeotropic distillation]]
* State Price Density in [[mathematical finance]]
* The information vector in the [[Information Filter]], [[GraphSLAM]], and a number of other algorithms used for [[robot localization]] and [[robotic mapping]].
* Used in [[Support-vector machine|Support Vector machines]] in cases where the data is not [[Linear separability|linearly separable]].
* Used in [[Microelectronics]] to represent the distance from a [[p-n junction]] to a point in the [[depletion region]] where the [[electric field]] is strongest.

==Other uses==
[[File:Net Serviços de Comunicação.svg|thumb|right|Ξ for E in a commercial logo]]
*''{{commons category-inline|Xi (letter)}}''
Uppercase Ξ is used as an 'E' to stylise company names/logos like [[Razer Inc|Razer]] (styled as '''RΛZΞR'''), [[Tesla, Inc.|Tesla]] (styled as '''TΞSLA'''), the presidential campaigns of [[Joe Biden 2020 presidential campaign|Joe Biden]] (styled as '''BIDΞN'''), musician [[Banners (musician)|Banners]] (styled as '''BANNΞRS'''), and in South Korean boy group [[ZE:A]]'s newest logo (styled as "ZΞA") (Compare: [[Heavy Metal umlaut]]; [[Faux Cyrillic]])

== Unicode ==
Unicode Code Charts: [https://www.unicode.org/charts/PDF/U0370.pdf Greek and Coptic (Range: 0370-03FF)]

* {{unichar|039E|html=}} ({{code|\Xi}} in TeX)
* {{unichar|03BE|html=}} ({{code|\xi}} in TeX)
* {{unichar|2C9C}}
* {{unichar|2C9D}}
* {{unichar|1D6B5}}{{efn|The {{sc|mathematical}} symbols should only be used for math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.}}
* {{unichar|1D6CF}}
* {{unichar|1D6EF}}
* {{unichar|1D709}}
* {{unichar|1D729}}
* {{unichar|1D743}}
* {{unichar|1D763}}
* {{unichar|1D77D}}
* {{unichar|1D79D}}
* {{unichar|1D7B7}}
{{notelist}}

== References ==
<references/>

== External links ==
{{Wiktionary|Ξ|ξ}}
* {{Commons category inline}}

[[Category:Greek letters]]