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|Use in other languages|
Xi is the 14th letter of the Greek alphabet (uppercase Ξ, lowercase ξ; Greek: ξι), representing the voiceless consonant cluster IPA: [ks]. Its name is pronounced [ksi] in Modern Greek, and generally /zaɪ/ or /ksaɪ/ in English. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh .
Xi is distinct from the letter chi, which gave its form to the Latin letter X.
Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the consonant cluster /ks/. In some 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, used for /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.
The Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Ѯ, ѯ).
Mathematics and science
The uppercase letter Ξ is used as a symbol in various contexts.
- Harish-Chandra's Ξ function in harmonic analysis and representation theory
- The Riemann Xi function in analytic number theory and complex analysis
- The "cascade particles" in particle physics
- The partition function under the grand canonical ensemble in statistical mechanics
- Indicating "no change of state" in Z notation in computing
- Monetary units of the cryptocurrencies Ether (and less commonly ETC), equal to 1018 Wei
The lowercase letter ξ is used as a symbol for:
- Random variables
- 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.
- The initial mass function in astronomy.
- The correlation function in astronomy.
- Spatial frequency; also sometimes temporal frequency.
- A small displacement in MHD plasma stability theory
- The x-coordinate of computational space as used in computational fluid dynamics
- Potential difference in physics (in volts)
- The radial integral in the spin-orbit matrix operator in atomic physics.
- The Killing vector in general relativity.
- Average logarithmic energy decrement per collision (neutron calculations in nuclear physics)
- 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
- Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus
- Extent of reaction, a concept in physical chemistry used often in chemical engineering kinetics and thermochemistry
- Unknown stereochemistry or stereocentre configuration in a planar ring system in organic chemistry, as well as uppercase Xi for unknown R/S/E/Z configuration in general
- One of the two different polypeptide chains of the human embryonic hemoglobin types Hb-Portland (ξ2γ2) and Hb-Gower I (ξ2ε2)
- 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 machines in cases where the data is not 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.
Greek Xi / Coptic Ksi
Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)
|Unicode name||GREEK CAPITAL LETTER XI||GREEK LOWERCASE LETTER XI||COPTIC CAPITAL LETTER KSI||COPTIC LOWERCASE LETTER KSI|
|UTF-8||206 158||CE 9E||206 190||CE BE||226 178 156||E2 B2 9C||226 178 157||E2 B2 9D|
|Numeric character reference||Ξ
|Named character reference||Ξ||ξ|
The following characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
|Unicode name||MATHEMATICAL BOLD
|MATHEMATICAL BOLD ITALIC
|MATHEMATICAL BOLD ITALIC|
|UTF-8||240 157 154 181||F0 9D 9A B5||240 157 155 143||F0 9D 9B 8F||240 157 155 175||F0 9D 9B AF||240 157 156 137||F0 9D 9C 89||240 157 156 169||F0 9D 9C A9||240 157 157 131||F0 9D 9D 83|
|UTF-16||55349 57013||D835 DEB5||55349 57039||D835 DECF||55349 57071||D835 DEEF||55349 57097||D835 DF09||55349 57129||D835 DF29||55349 57155||D835 DF43|
|Numeric character reference||𝚵
|Unicode name||MATHEMATICAL SANS-SERIF
BOLD CAPITAL XI
BOLD LOWERCASE XI
BOLD ITALIC CAPITAL XI
BOLD ITALIC LOWERCASE XI
|UTF-8||240 157 157 163||F0 9D 9D A3||240 157 157 189||F0 9D 9D BD||240 157 158 157||F0 9D 9E 9D||240 157 158 183||F0 9D 9E B7|
|UTF-16||55349 57187||D835 DF63||55349 57213||D835 DF7D||55349 57245||D835 DF9D||55349 57271||D835 DFB7|
|Numeric character reference||𝝣
- Media related to Xi (letter) at Wikimedia Commons
Uppercase Ξ is used as an 'E' to stylise company names/logos like Razer (styled as RΛZΞR), Tesla (styled as TΞSLA), 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)
- ^ "xi". New Oxford American Dictionary, 2nd Edition.
- ^ SPIE Optipedia article: "Spatial Frequency"
- ^ IUPAC Gold Book Entry: "Extent of Reaction" Archived June 29, 2012, at the Wayback Machine
- ^ John Buckingham; Caroline M. Cooper; Rupert Purchase (18 November 2015). Natural Products Desk Reference. CRC Press. pp. 53–. ISBN 978-1-4398-7362-5.
- ^ Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names. 2014. pp. 1159–1160. ISBN 9780854041824. Retrieved 11 September 2017.