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Xi (uppercase Ξ, lowercase ξ; Greek: ξι) is the 14th letter of the Greek alphabet. It is pronounced [ksi] in Modern Greek, and generally // or // in English. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh .
Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the sound [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 sound [ks] was represented by Χ (which in classical Greek is chi, used for /kʰ/). Because this variant of the Greek alphabet was used in Italy, the Latin alphabet borrowed Χ rather than Ξ as the Latin letter X.
Mathematics and science
The uppercase letter Ξ is used as symbol for:
- The "cascade particles" in particle physics
- Indicating "no change of state" in Z notation
- The partition function under the grand canonical ensemble in statistical mechanics
- Harish-Chandra's Ξ function
- The Riemann Xi function
- Monetary units of the cryptocurrency Ether, equal to 1018 Wei
The lowercase letter ξ is used as a symbol for:
- Random variables
- Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus
- Dimensionless distance variable used in the Lane–Emden equation
- 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
- Damping Ratio C/Ccr(vibrational analysis)
- 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
- One of the two different polypeptide chains of the human embryonic hemoglobin types Hb-Portland (ξ2γ2) and Hb-Gower I (ξ2ε2)
- 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
- A parameter denoted as warped time used to derive the equations for homogeneous azeotropic distillation
- 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
- State Price Density in mathematical finance
- The diameter of a crystal nucleus in nucleation theory
- Microturbulence velocity in a stellar atmosphere
- The information vector in the Information Filter, GraphSLAM, and a number of other algorithms used for robot localization and robotic mapping.
- The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics.
- Greek Xi / Coptic Ksi
|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||Ξ||ξ||ξ||Ⲝ||Ⲝ||ⲝ||ⲝ|
|Named character reference||Ξ||ξ|
- Mathematical Xi
|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||𝚵||𝛏||𝛏||𝛯||𝛯||𝜉||𝜉||𝜩||𝜩||𝝃||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||𝝣||𝝽||𝝽||𝞝||𝞝||𝞷||𝞷|
These 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.
- Media related to Letter "E" as "Ξ" at Wikimedia Commons
|Look up Ξ or ξ in Wiktionary, the free dictionary.|
- "xi". New Oxford American Dictionary, 2nd Edition.
- 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. p. 1159–1160. Retrieved 11 September 2017.
- SPIE Optipedia article: "Spatial Frequency"
- Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)